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

Author

Reinhard Zumkeller, Jul 19 2002

Keywords

• nonn
• look

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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.

Formula

a(n) >= A048250(n).