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A183097 a(n) = sum of powerful divisors d (including 1) of n. 5
1, 1, 1, 5, 1, 1, 1, 13, 10, 1, 1, 5, 1, 1, 1, 29, 1, 10, 1, 5, 1, 1, 1, 13, 26, 1, 37, 5, 1, 1, 1, 61, 1, 1, 1, 50, 1, 1, 1, 13, 1, 1, 1, 5, 10, 1, 1, 29, 50, 26, 1, 5, 1, 37, 1, 13, 1, 1, 1, 5, 1, 1, 10, 125, 1, 1, 1, 5, 1, 1, 1, 130, 1, 1, 26, 5, 1, 1, 1, 29, 118, 1, 1, 5, 1, 1, 1, 13, 1, 10, 1, 5, 1, 1, 1, 61, 1, 50, 10, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Sequence is not the same as A091051(n); a(72) = 130,  A091051(72) = 58.

a(n) = sum of divisors d of n from set A001694 - powerful numbers.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16385

Index entries for sequences related to sums of divisors

FORMULA

a(n) = A000203(n) - A183098(n) = A183100(n) + 1.

a(1) = 1, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = ((p^(k+1)-1) / (p-1))-p, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.

EXAMPLE

For n = 12, set of such divisors is {1, 4}; a(12) = 1+4 = 5.

MATHEMATICA

fun[p_, e_] := (p^(e+1)-1)/(p-1) - p; a[1] = 1; a[n_] := Times @@ (fun @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, May 14 2019 *)

PROG

(PARI) A183097(n) = sumdiv(n, d, ispowerful(d)*d); \\ Antti Karttunen, Oct 07 2017

CROSSREFS

Cf. A001694, A091051, A183102.

Sequence in context: A242404 A145295 A091051 * A285486 A230368 A256690

Adjacent sequences:  A183094 A183095 A183096 * A183098 A183099 A183100

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Dec 25 2010

STATUS

approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)