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 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 (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 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 January 19 19:49 EST 2019. Contains 319309 sequences. (Running on oeis4.)