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A126164 Sum of the proper exponential divisors of n. 8
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified October 19 15:49 EDT 2018. Contains 316365 sequences. (Running on oeis4.)