A253303 Smallest integer m such that gcd{x | sum of proper divisors of x is m} is equal to 2*n, when there are at least two such x's.

16, 136, 186, 1352, 1340, 1356, 1414, 1276, 1026, 15640, 6742, 1968, 35786, 924, 11076, 11812, 61714, 14556, 76862, 6440, 12774, 70444, 62446, 16080, 24904, 16152, 27900, 65464, 36026, 41100, 85810, 56008, 50142, 23152

Offset

1,1

Comments

Only integers m that satisfy A048138(m) > 1 are considered here.

Links

Table of n, a(n) for n=1..34.

Formula

a(n) = A253302(2*n).

Example

The integers whose sum of proper divisors is 16 are 12 and 26, and gcd(12, 26) is 2, so a(1) = 16 (see Example section of A152454).

Prog

(PARI) build(nb) = {vs = vector(nb); nc = nb^2; forcomposite(n=2, nc, val = sigma(n)-n; if (val <= nb, if (vs[val] == 0, vs[val] = -n, vs[val] = gcd(vs[val], n)); ); ); vs[1] = 1; vs; }
lista() = {vd = build(100000); vmax = 80; vr = vector(vmax); forstep (ig=2, vmax, 2, for (i=1, #vd, w = vd[i]; if (w ==ig, vr[ig] = i; break; ); ); ); forstep (i=2, #vr, 2, if (vr[i] == 0, break, print1(vr[i], ", "))); }

Crossrefs

Cf. A001065 (sum of proper divisors), A048138, A152454, A253302.

Sequence in context: A110274 A067814 A219904 * A139616 A304506 A187175

Adjacent sequences: A253300 A253301 A253302 * A253304 A253305 A253306

Keyword

nonn,more

Author

Michel Marcus, Dec 30 2014

Status

approved