A052343 -id:A052343 - cp's OEIS frontend

A357070 Number of partitions of n into at most 2 distinct positive triangular numbers.

1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 1, 0, 2, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 2, 0, 0, 0, 2, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 3, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 1, 1, 1

Offset: 0

Ilya Gutkovskiy, Oct 25 2022

nonn

Cf. A000217, A024940, A052343, A307597, A347730, A357071, A357072.

A347628 Number of partitions of n into at most 6 triangular numbers.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 4, 3, 3, 4, 5, 4, 6, 6, 5, 8, 8, 6, 9, 9, 8, 11, 11, 9, 13, 13, 11, 13, 15, 12, 17, 17, 14, 19, 19, 16, 20, 21, 18, 22, 24, 19, 25, 26, 22, 26, 29, 24, 30, 31, 26, 33, 34, 28, 33, 36, 30, 37, 40, 33, 41, 43, 36, 40, 45, 38

Offset: 0

Ilya Gutkovskiy, Sep 09 2021

nonn

Cf. A000217, A002636, A007294, A052343, A110534, A319816, A347627.

A274794 Numbers n such that n^3 is the sum of two triangular numbers in exactly one way.

Original entry on oeis.org

0, 1, 3, 4, 7, 9, 10, 19, 24, 25, 34, 37, 39, 42, 49, 54, 55, 72, 73, 78, 85, 87, 93, 94, 102, 108, 109, 118, 138, 142, 147, 157, 160, 165, 168, 175, 192, 195, 202, 210, 214, 220, 228, 232, 243, 247, 249, 250, 252, 253, 258, 267, 273, 274, 279, 289, 297, 312, 333

Offset: 1

Altug Alkan, Jul 07 2016

nonn

A115104 is a subsequence. Terms such that 4*n^3 + 1 is not prime are 24, 337, 457, 750, 840, 1015, ...

			3 is a term because 3^3 = 27 = 6 + 21.

Cf. A000217, A000578, A020756, A052343, A115104, A119345.

Select[Range@ 333, Length[PowersRepresentations[4 #^3 + 1, 2, 2]] == 1 &] (* after Ant King at A052343, or *)
nn = 20; t = (#^2 + #)/2 & /@ Range[0, nn^3]; Select[Range[0, nn], Function[n, Count[Transpose@ {#, n^3 - #} &@ Range[0, Floor[n^3/2]], k_ /; Times @@ Boole@ Map[MemberQ[t, #] &, k] == 1] == 1]] (* Michael De Vlieger, Jul 07 2016 *)

a052343(n) = sum(i=0, (sqrtint(4*n + 1) - 1)\2, issquare(n - i - i^2));
lista(nn) = for(n=0, nn, if(a052343(n^3) == 1, print1(n, ", ")));

cp's OEIS Frontend

A357070 Number of partitions of n into at most 2 distinct positive triangular numbers.

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A347628 Number of partitions of n into at most 6 triangular numbers.

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A274794 Numbers n such that n^3 is the sum of two triangular numbers in exactly one way.

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