

A126164


Sum of the proper exponential divisors of n.


10



0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 6, 0, 0, 0, 6, 0, 6, 0, 10, 0, 0, 0, 6, 5, 0, 3, 14, 0, 0, 0, 2, 0, 0, 0, 36, 0, 0, 0, 10, 0, 0, 0, 22, 15, 0, 0, 18, 7, 10, 0, 26, 0, 6, 0, 14, 0, 0, 0, 30, 0, 0, 21, 14, 0, 0, 0, 34, 0, 0, 0, 48, 0, 0, 15
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OFFSET

1,4


COMMENTS

The edivisors (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, eDivisor.


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.


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
A126164(n) = (A051377(n)  n); \\ Antti Karttunen, Oct 04 2017, after the given formula


CROSSREFS

Cf. A051377, A049419, A054979, A054980, A126168.
Sequence in context: A263145 A057108 A063958 * A145007 A228616 A151670
Adjacent sequences: A126161 A126162 A126163 * A126165 A126166 A126167


KEYWORD

easy,nonn


AUTHOR

Ant King, Dec 21 2006


STATUS

approved



