A380436 Integers with at least 1 proper factorization for which the sum of the squares of the factors is a square.

12, 16, 32, 36, 48, 60, 80, 81, 96, 108, 112, 120, 128, 140, 144, 168, 192, 220, 224, 240, 252, 256, 288, 300, 320, 336, 351, 360, 364, 396, 400, 420, 432, 448, 480, 486, 500, 512, 528, 540, 544, 560, 576, 588, 608, 612, 624, 625, 640, 644, 648, 660, 672, 704

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Sean A. Irvine, Java program (github)

Example

a(1) = 12: {3, 4} (3 * 4 = 12 and 3^2 + 4^2 = 5^2).
a(2) = 16: {2, 2, 2, 2} (2 * 2 * 2 * 2 = 16 and 2^2 + 2^2 + 2^2 + 2^2 = 4^2).
a(3) = 32: {2, 4, 4} (2 * 4 * 4 = 32 and 2^2 + 4^2 + 4^2 = 6^2).

Prog

(PARI) a380436_count(x, f=List())={my(r=x/if(#f, vecprod(Vec(f)), 1)); if(r==1, return(if(issquare(sum(i=1, #f, f[i]^2)), 1, 0))); my(d, c=0); fordiv(r, d, if(d==1 || d==x || (#f && d<f[#f]), next); listput(f, d); c+=a380436_count(x, f); listpop(f)); return(c)} \\ Charles L. Hohn, Mar 09 2025

Crossrefs

A118903 is a subsequence.

Sequence in context: A109240 A020740 A344021 * A086980 A256934 A343153

Adjacent sequences: A380433 A380434 A380435 * A380437 A380438 A380439

Keyword

nonn

Author

Charles L. Hohn, Jan 24 2025

Status

approved