OFFSET
1,4
COMMENTS
The e-divisors (or exponential divisors) of x=Product p(i)^r(i) are all numbers of the form Product p(i)^s(i) where s(i) divides r(i) for all i.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
Ant King, Mathematica programs for A126164 - A126166.
Eric Weisstein's World of Mathematics, e-Divisor.
FORMULA
a(n) = esigma(n) - n = A051377(n) - n.
EXAMPLE
The exponential divisors of 240 are 30, 60 and 240, so a(240) = 30+60 = 90.
MATHEMATICA
f[p_, e_] := DivisorSum[e, p^# &]; a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - n; Array[a, 100] (* Amiram Eldar, Aug 13 2023 *)
PROG
(PARI)
A051377(n) = { my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2], d, f[i, 1]^d)); }; \\ This function from Charles R Greathouse IV, Nov 22 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ant King, Dec 21 2006
STATUS
approved