

A178645


a(n) = sum of divisors d of n such that d^k is not equal to n for any k >= 1.


1



0, 1, 1, 1, 1, 6, 1, 5, 1, 8, 1, 16, 1, 10, 9, 9, 1, 21, 1, 22, 11, 14, 1, 36, 1, 16, 10, 28, 1, 42, 1, 29, 15, 20, 13, 49, 1, 22, 17, 50, 1, 54, 1, 40, 33, 26, 1, 76, 1, 43, 21, 46, 1, 66, 17, 64, 23, 32, 1, 108, 1, 34, 41, 49, 19, 78, 1, 58, 27, 74, 1, 123, 1, 40, 49, 64, 19, 90, 1, 106, 28, 44, 1, 140, 23, 46, 33, 92, 1, 144, 21, 76, 35, 50, 25, 156, 1, 73, 57, 107
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OFFSET

1,6


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sums of divisors


FORMULA

a(n) = A000203(n)  A175067(n).
a(1) = 0, a(p) = 1, a(pq) = p+q+1, a(pq...z) = [(p+1)*(q+1)*…*(z+1)]  (pq…z), for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.


EXAMPLE

For n = 16, set of such divisors is {1, 8}; a(16) = 1+8=9.
For n = 90, which is not a perfect power (A001597), the only divisor d for which d^k = 90 is 90 itself, with k=1, thus a(90) = A001065(90) = A000203(90)  90 = 144.  Antti Karttunen, Jun 12 2018


PROG

(PARI)
A175070(n) = if(!ispower(n), 0, sumdiv(n, d, if((d>1)&&(d<n)&&((d^valuation(n, d))==n), d, 0)));
A178645(n) = (sigma(n)  (A175070(n) + n)); \\ Antti Karttunen, Jun 12 2018


CROSSREFS

Cf. A000203, A001065, A175067, A175070.
Sequence in context: A016534 A230821 A160135 * A010137 A245967 A212006
Adjacent sequences: A178642 A178643 A178644 * A178646 A178647 A178648


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Dec 25 2010


EXTENSIONS

Term a(90) corrected from 204 to 144 by Antti Karttunen, Jun 12 2018


STATUS

approved



