A253303 - OEIS

%I #27 Aug 01 2019 03:47:18

%S 16,136,186,1352,1340,1356,1414,1276,1026,15640,6742,1968,35786,924,

%T 11076,11812,61714,14556,76862,6440,12774,70444,62446,16080,24904,

%U 16152,27900,65464,36026,41100,85810,56008,50142,23152

%N 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.

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

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

%e 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).

%o (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;}

%o 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], ", ")));}

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

%K nonn,more

%O 1,1

%A _Michel Marcus_, Dec 30 2014