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A162296 Sum of divisors of n that have a square factor. 24
0, 0, 0, 4, 0, 0, 0, 12, 9, 0, 0, 16, 0, 0, 0, 28, 0, 27, 0, 24, 0, 0, 0, 48, 25, 0, 36, 32, 0, 0, 0, 60, 0, 0, 0, 79, 0, 0, 0, 72, 0, 0, 0, 48, 54, 0, 0, 112, 49, 75, 0, 56, 0, 108, 0, 96, 0, 0, 0, 96, 0, 0, 72, 124, 0, 0, 0, 72, 0, 0, 0, 183, 0, 0, 100, 80, 0, 0, 0, 168, 117, 0, 0, 128, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Note that 1 does not have a square factor. - Antti Karttunen, Nov 20 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sums of divisors.

FORMULA

a(n) + A048250(n) = A000203(n). - Antti Karttunen, Nov 20 2017

From Amiram Eldar, Oct 01 2022: (Start)

a(n) = 0 iff n is squarefree (A005117).

a(n) = n iff n is a square of a prime (A001248).

Sum_{k=1..n} a(k) ~ (Pi^2/12 - 1/2) * n^2. (End)

EXAMPLE

a(8) = 12 = 4 + 8.

MATHEMATICA

Array[DivisorSum[#, # &, # (1 - MoebiusMu[#]^2) == # &] &, 86] (* Michael De Vlieger, Nov 20 2017 *)

a[1]=0; a[n_] := DivisorSigma[1, n] - Times@@(1+FactorInteger[n][[;; , 1]]); Array[a, 86] (* Amiram Eldar, Dec 20 2018 *)

PROG

(PARI) a(n)=sumdiv(n, d, d*(1-moebius(d)^2)); v=vector(300, n, a(n))

CROSSREFS

Cf. A000203, A001248, A005117, A013929, A048250.

Sequence in context: A126849 A284117 A183099 * A169773 A236380 A298825

Adjacent sequences:  A162293 A162294 A162295 * A162297 A162298 A162299

KEYWORD

easy,nonn,changed

AUTHOR

Joerg Arndt, Jun 30 2009

STATUS

approved

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Last modified October 7 09:17 EDT 2022. Contains 357270 sequences. (Running on oeis4.)