# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a073181 Showing 1-1 of 1 %I A073181 #14 Jul 09 2022 11:09:27 %S A073181 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, %T A073181 4,28,30,72,32,3,48,54,48,16,38,60,56,30,42,96,44,40,33,72,48,16,8,18, %U A073181 72,46,54,12,72,36,80,90,60,108,62,96,41,3,84,144,68,58,96,144,72,16,74 %N A073181 Sum of divisors of n which are not greater than the squarefree kernel of n. %H A073181 Antti Karttunen, Table of n, a(n) for n = 1..10000 %F A073181 a(n) >= A048250(n). %e A073181 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. %t A073181 a[n_] := DivisorSum[n, # &, # <= Times @@ FactorInteger[n][[;;, 1]] &]; Array[a, 100] (* _Amiram Eldar_, Jul 09 2022 *) %o A073181 (PARI) %o A073181 A007947(n) = factorback(factorint(n)[, 1]); \\ This function from _Andrew Lelechenko_ %o A073181 A073181(n) = sumdiv(n, d, d*(d<=A007947(n))); \\ _Antti Karttunen_, Sep 10 2017, after _Michel Marcus_'s code for A073183. %Y A073181 Cf. A000203, A007947, A048250, A073180, A073183. %K A073181 nonn,look %O A073181 1,2 %A A073181 _Reinhard Zumkeller_, Jul 19 2002 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE