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

2,5

Comments

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

Links

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

Formula

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

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

Example

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

Prog

(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])));

Crossrefs

Cf. A001065, A152454.

Cf. A070015, A135244.

Cf. A005114, A057709.

Sequence in context: A240952 A221749 A055967 * A317447 A202582 A292605

Adjacent sequences: A366107 A366108 A366109 * A366111 A366112 A366113

Keyword

nonn

Author

Michel Marcus, Oct 28 2023

Status

approved