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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).
1
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
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
Sequence in context: A086012 A248394 A368843 * A252459 A083918 A083895
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 27 2007
EXTENSIONS
More terms from R. J. Mathar, Nov 01 2007
STATUS
approved