A253302 Smallest integer m such that gcd{x | sum of proper divisors of x is m} is equal to n, when there are at least two such x's.

1, 16, 300, 136, 50316, 186, 97748, 1352, 72318, 1340, 1652, 1356

Offset: 1

Author

Michel Marcus, Dec 30 2014

Keywords

• nonn
• more

Comments

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

Other known terms with odd indices: a(25)=39926, a(49)=46850.

For terms with even indices see A253303.

Examples

			For every prime p the sum of proper divisors of p is 1, and the GCD of the primes is 1, so a(1) = 1.
		

Crossrefs

Cf. A001065 (sum of proper divisors), A048138, A152454, A253303.

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 = 20; vr = vector(vmax); for (ig=1, vmax, for (i=1, #vd, w = vd[i]; if (w ==ig, vr[ig] = i; break;););); for (i=1, #vr, if (vr[i] == 0, break, print1(vr[i], ", ")));}

Extensions

a(1)=1 suggested by Robert Israel, Jan 01 2015