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A295295 Sum of squarefree divisors of the powerful part of n: a(n) = A048250(A057521(n)). 3
1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 6, 1, 4, 3, 1, 1, 1, 3, 1, 1, 1, 12, 1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 3, 8, 6, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 4, 3, 1, 1, 1, 3, 1, 1, 1, 12, 1, 1, 6, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 8, 4, 18, 1, 1, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

Index entries for sequences related to sums of divisors

FORMULA

Multiplicative with a(p) = 1 and a(p^e) = (p+1) for e > 1.

a(n) = A048250(A057521(n)) = A048250(A064549(A003557(n))).

a(n) = A048250(n) / A092261(n).

MATHEMATICA

Array[DivisorSum[#/Denominator[#/Apply[Times, FactorInteger[#][[All, 1]]]^2], # &, SquareFreeQ] &, 105] (* Michael De Vlieger, Nov 26 2017, after Jean-Fran├žois Alcover at A057521 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A295295 n) (if (= 1 n) n (let ((p (A020639 n)) (e (A067029 n))) (* (if (= 1 e) 1 (+ 1 p)) (A295295 (A028234 n))))))

(PARI) a(n) = my(f=factor(n)); for (i=1, #f~, if (f[i, 2]==1, f[i, 1]=1)); sumdiv(factorback(f), d, d*issquarefree(d)); \\ Michel Marcus, Jan 29 2021

CROSSREFS

Cf. A000203, A003557, A048250, A057521, A064549, A092261, A295294.

Sequence in context: A166030 A191523 A132890 * A069290 A348660 A076476

Adjacent sequences:  A295292 A295293 A295294 * A295296 A295297 A295298

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Nov 25 2017

STATUS

approved

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Last modified January 17 10:21 EST 2022. Contains 350387 sequences. (Running on oeis4.)