A270816 For each primary pseudoperfect number n, this sequence gives the sum of (n/p + 1)/p for every prime divisor p of n.

1, 3, 17, 691, 17521, 824473683, 19579678305, 3161039281414579992004338982115

Offset: 1

Author

Paolo P. Lava, Mar 23 2016

Keywords

• nonn
• more

Examples

			Prime factors of 42 are 2, 3 and 7: (42/2 + 1)/2 + (42/3 + 1)/3 + (42/7 + 1)/7 = 11 + 5 + 1 = 17.
		

Crossrefs

Cf. A054377, A270815.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,k,n,x;
x:=[2, 6, 42, 1806, 47058, 2214502422, 52495396602, 8490421583559688410706771261086];
for n from 1 to nops(x) do a:=ifactors(x[n])[2];
b:=add((x[n]/a[k][1]+1)/a[k][1],k=1..nops(a)); print(b);
od; end: P(10^4);

Formula

a(k) = Sum_{prime p|n(k)} (n(k)/p + 1)/p, where n(k) = A054377(k).