A366110 a(n) is the difference between the maximum and minimum number whose proper divisors sum to n, or 0 if there is no such number.

0, 0, 0, 0, 19, 0, 39, 0, 0, 0, 0, 8, 147, 17, 14, 16, 0, 12, 327, 73, 18, 28, 0, 48, 0, 64, 0, 72, 0, 189, 903, 202, 0, 160, 0, 168, 0, 0, 37, 328, 1651, 387, 1767, 280, 34, 364, 0, 476, 54, 448, 0, 432, 2767, 677, 0, 604, 0, 432, 0, 528, 3603, 753, 66, 826, 0, 768, 0, 720, 0

Offset: 2

Author

Michel Marcus, Oct 28 2023

Keywords

• nonn

Comments

A152454 is the irregular triangle in which row n lists the numbers whose proper divisors sum to n.

Examples

			A152454 begins as []; [4]; [9]; []; [6, 25]; [8]; [10, 49]...
so sequence begins 0, 0, 0, 0, 19, 0, 39, ...
		

Links

• Michel Marcus, Table of n, a(n) for n = 2..10001

Crossrefs

Cf. A001065, A152454.

Cf. A070015, A135244.

Cf. A005114, A057709.

Programs

PARI

lista(nn) = my(v = vector(nn, k, [])); forcomposite (i=1, nn^2, my(x=sigma(i)-i); if (x <=  nn, v[x] = concat(v[x], i));); vector(nn-1, k, k++; if (#v[k], vecmax(v[k]) - vecmin(v[k])));

Formula

a(n) = A135244(n) - A070015(n).

a(A005114(n)) = a(A057709(n)) = 0.