A073181 Sum of divisors of n which are not greater than the squarefree kernel of n.

1, 3, 4, 3, 6, 12, 8, 3, 4, 18, 12, 16, 14, 24, 24, 3, 18, 12, 20, 22, 32, 36, 24, 16, 6, 42, 4, 28, 30, 72, 32, 3, 48, 54, 48, 16, 38, 60, 56, 30, 42, 96, 44, 40, 33, 72, 48, 16, 8, 18, 72, 46, 54, 12, 72, 36, 80, 90, 60, 108, 62, 96, 41, 3, 84, 144, 68, 58, 96, 144, 72, 16, 74

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) >= A048250(n).

Example

The squarefree kernel of 56 = 7 * 2^3 is 14 = 7*2 and the divisors <= 14 of 56 are {1, 2, 4, 7, 8, 14}, therefore a(56) = 1 + 2 + 4 + 7 + 8 + 14 = 36.

Mathematica

a[n_] := DivisorSum[n, # &, # <= Times @@ FactorInteger[n][[;; , 1]] &]; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)

Prog

(PARI)
A007947(n) = factorback(factorint(n)[, 1]); \\ This function from Andrew Lelechenko
A073181(n) = sumdiv(n, d, d*(d<=A007947(n))); \\ Antti Karttunen, Sep 10 2017, after Michel Marcus's code for A073183.

Crossrefs

Cf. A000203, A007947, A048250, A073180, A073183.

Sequence in context: A367503 A048250 A323363 * A183100 A340323 A046897

Adjacent sequences: A073178 A073179 A073180 * A073182 A073183 A073184

Keyword

nonn,look

Author

Reinhard Zumkeller, Jul 19 2002

Status

approved