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

Author

Michel Marcus, Dec 30 2014

Keywords

• nonn
• more

Comments

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

Examples

			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).
		

Crossrefs

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

Programs

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], ", ")));}

Formula

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