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

Author

Charles L. Hohn, Jan 24 2025

Keywords

• nonn

Examples

			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).
		

Links

• Sean A. Irvine, Java program (github)

Crossrefs

A118903 is a subsequence.

Programs

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 && dCharles L. Hohn, Mar 09 2025