

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.


3



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
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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



