A289895 Numbers that are the sum of distinct square pyramidal numbers (A000330).

0, 1, 5, 6, 14, 15, 19, 20, 30, 31, 35, 36, 44, 45, 49, 50, 55, 56, 60, 61, 69, 70, 74, 75, 85, 86, 90, 91, 92, 96, 97, 99, 100, 104, 105, 106, 110, 111, 121, 122, 126, 127, 135, 136, 140, 141, 145, 146, 147, 151, 152, 154, 155, 159, 160, 161, 165, 166, 170, 171, 175, 176, 177, 181, 182, 184, 185, 189, 190, 191, 195, 196, 200

Offset

1,3

Comments

It appears that 1528 is the largest of 306 positive integers not in this sequence.

Links

Table of n, a(n) for n=1..73.

Index entries for sequences related to sums of squares

Index to sequences related to pyramidal numbers

Formula

Exponents in expansion of Product_{k>=1} (1 + x^(k*(k+1)*(2*k+1)/6)).

Example

20 is in the sequence because 20 = 1 + 5 + 14 = 1^2 + 1^2 + 2^2 + 1^2 + 2^2 + 3^2.

Mathematica

max = 200; f[x_] := Product[1 + x^(k (k + 1) (2 k + 1)/6), {k, 1, 10}]; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, max}]]

Crossrefs

Cf. A000330, A003995.

Sequence in context: A314292 A294572 A084381 * A335785 A266304 A359329

Adjacent sequences: A289892 A289893 A289894 * A289896 A289897 A289898

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 14 2017

Status

approved