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
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.
Programs
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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).