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

1,2

Links

Table of n, a(n) for n=1..8.

Formula

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

Example

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.

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);

Crossrefs

Cf. A054377, A270815.

Sequence in context: A049985 A126579 A309060 * A217957 A252730 A362647

Adjacent sequences: A270813 A270814 A270815 * A270817 A270818 A270819

Keyword

nonn,more

Author

Paolo P. Lava, Mar 23 2016

Status

approved