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A figurate number of the form P_n^((4))=1/6n(n+1)(2n+1), (1) corresponding to a configuration of points which form a square pyramid, is called a square pyramidal number (or ...

The nth taxicab number Ta(n) is the smallest number representable in n ways as a sum of positive cubes. The numbers derive their name from the Hardy-Ramanujan number Ta(2) = ...

A Thâbit ibn Kurrah number, sometimes called a 321-number, is a number of the form K_n=3·2^n-1. The first few for n=0, 1, ... are 2, 5, 11, 23, 47, 95, 191, 383, 767, ... ...

A Sierpiński number of the first kind is a number of the form S_n=n^n+1. The first few are 2, 5, 28, 257, 3126, 46657, 823544, 16777217, ... (OEIS A014566). Sierpiński proved ...

A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...

A biquadratic number is a fourth power, n^4. The first few biquadratic numbers are 1, 16, 81, 256, 625, ... (OEIS A000583). The minimum number of biquadratic numbers needed ...

A pentagonal square triangular number is a number that is simultaneously a pentagonal number P_l, a square number S_m, and a triangular number T_n. This requires a solution ...

Number Theory

An odd alternating permutation number, more commonly called an Euler number or secant number.

A cubic number is a figurate number of the form n^3 with n a positive integer. The first few are 1, 8, 27, 64, 125, 216, 343, ... (OEIS A000578). The protagonist Christopher ...