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# Multi-Polygonal Numbers

# Heptagonal Triangular Numbers

A number which is simultaneously a heptagonal number and a triangular number. The First few are

1,

55, 121771, 5720653, 12625478965,

A number which is simultaneously a heptagonal number and a

Square Number. The First few are

1,

81, 5929, 2307361, 168662169, 12328771225,

# Heptagonal Pentagonal Numbers

A number which is simultaneously a heptagonal number and a pentagonal number. The First few are

1, 4347, 16701685, 64167869935, 246532939589097,

# Heptagonal Hexagonal Numbers

A number which is simultaneously a heptagonal number and hexagonal number. The First few are

1, 121771, 12625478965, 1309034909945503,

# Heptagonal Octagonal Numbers

A number which is simultaneously a heptagonal number and an octagonal number. The First few are

1, 297045, 69010153345,

# Heptagonal Pentagonal Numbers

A number which is simultaneously a heptagonal number and a pentagonal number. The First few are

1, 40755, 1533776805, 57722156241751, ...

# Octagonal Triangular Numbers

A number which is simultaneously an octagonal number and a Triangular number. The First few are

1,

21, 11781, 203841, 113123361, ...

A number which is simultaneously an octagonal number and a

Square Number. The First few are

1,

225, 43681, 8473921, 1643897025, ...

# Octagonal Pentagonal Numbers

A number which is simultaneously an octagonal number and a pentagonal number. The First few are

1,

176, 1575425, 234631320, 2098015778145, ...

# Octagonal Hexagonal Numbers

A number which is simultaneously an octagonal number and a hexagonal number. The First few are

1, 11781, 113123361, 1086210502741, ...

# Pentagonal Triangular Numbers

A number which is simultaneously a pentagonal number and a triangular number. The First few are

1,

210, 40755, 7906276, 1533776805,

A number which is simultaneously a pentagonal number and a

Square Number. The First few are

1, 9801, 94109401, 903638458801, 8676736387298001, ...

# Square Triangular Numbers

A number which is simultaneously a

Square Number and a triangular number. The First few are

1,

36,

1225, 41616, 1413721, 48024900, ...

# Nonagonal Octagonal Numbers

A number which is simultaneously a nonagonal number and an octagonal number. The First few are

1, 631125, 286703855361, 130242107189808901, ...

# Nonagonal Heptagonal Numbers

A number which is simultaneously a nonagonal number and a heptagonal number. The First few are

1, 26884, 542041975, 10928650279834, ...

# Nonagonal Hexagonal Numbers

A number which is simultaneously a nonagonal number and a hexagonal number. The First few are

1,

325, 5330229625, 1353857339341, 22184715227362706161, ...

# Nonagonal Pentagonal Numbers

A number which is simultaneously a nonagonal number and a pentagonal number. The First few are

1,

651, 180868051, 95317119801, 26472137730696901, ...

A number which is simultaneously a nonagonal number and a

Square Number. The First few are

1,

9,

1089, 8281, 978121, 7436529, ...

# Nonagonal Triangular Numbers

A number which is simultaneously a nonagonal number and a triangle number. The First few are

1,

325, 82621, 20985481, 5330229625, 1353857339341, ...

The only numbers which are simultaneously square and tetrahedral are

1,

4 and 19600.

# Tetrahedal and Triangular Numbers

The only numbers which are simultaneously triangular and tetrahedral are

1,

10,

120,

1540 and 7140.

The only numbers which are simultaneously square and square pyramidal are

1 and 4900.

# Square Pyramidal and Triangular Numbers

The only numbers which are simultaneously triangular and square pyramidal are

1,

55,

91, 208335.

# Square Pyramidal and Tetrahedal Numbers

The only number which is simultaneously tetrahedal and square pyramidal is

1.

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