A127268 If the prime factorization of n is n = Product_{p|n} p^b(p,n) (p = distinct prime divisors of n, each b(p,n) is a positive integer), then a(n) is (Sum_{p|n} p^b(p,n)) taken mod (Sum_{p|n} p).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 2, 6, 0, 0, 4, 0, 6, 0, 2, 0, 4, 0, 6, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 6, 0, 2, 0, 0, 0, 0, 0, 6, 6, 1

Offset

1,12

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A008475(n) mod A008472(n), if n > 1. - R. J. Mathar, Nov 01 2007

Example

40 = 2^3 *5^1. So a(40) = 2^3 + 5^1 (mod (2+5)) = 13 (mod 7) = 6.

Maple

A008475 := proc(n) local ifs ; if n =1 then 0; else ifs := ifactors(n)[2] ; add(op(1, i)^op(2, i), i =ifs) ; fi ; end: A008472 := proc(n) local ifs ; if n =1 then 0; else ifs := ifactors(n)[2] ; add(op(1, i), i =ifs) ; fi ; end: A127268 := proc(n) if n = 1 then 0 ; else A008475(n) mod A008472(n) ; fi ; end: seq(A127268(n), n=1..100) ; # R. J. Mathar, Nov 01 2007

Mathematica

Array[Mod[Total@ Apply[Power, # /. {1, 1} -> {0, 1}, 1], Total[#[[All, 1]] ]] &@ FactorInteger[#] &, 100] (* Michael De Vlieger, Nov 20 2017 *)

Prog

(PARI)
A008472(n) = vecsum(factor(n)[, 1]); \\ This function from M. F. Hasler, Jul 18 2015
A008475(n) = { my(f=factor(n)); vecsum(vector(#f~, i, f[i, 1]^f[i, 2])); };
A127268(n) = if(1==n, 0, (A008475(n) % A008472(n))); \\ Antti Karttunen, Nov 20 2017

Crossrefs

Cf. A008472, A008475.

Sequence in context: A086012 A248394 A368843 * A252459 A083918 A083895

Adjacent sequences: A127265 A127266 A127267 * A127269 A127270 A127271

Keyword

nonn

Author

Leroy Quet, Mar 27 2007

Extensions

More terms from R. J. Mathar, Nov 01 2007

Status

approved