login
A373480
a(n) = A003415(n) mod A001414(n), where A003415 is the arithmetic derivative, and A001414 is the sum of prime factors with multiplicity.
3
1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 5, 1, 6, 0, 0, 1, 8, 0, 0, 0, 10, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 5, 1, 3, 6, 0, 1, 2, 0, 9, 0, 5, 1, 4, 0, 1, 0, 0, 1, 8, 1, 0, 12, 0, 0, 13, 1, 9, 0, 3, 1, 0, 1, 0, 3, 11, 0, 17, 1, 7, 0, 0, 1, 12, 0, 0, 0, 4, 1, 6, 0, 15, 0, 0, 0, 12, 1, 13, 7, 0, 1, 3, 1, 12, 11
OFFSET
2,11
LINKS
MATHEMATICA
Array[Mod[If[#1 < 2, 0, #1 Total[#2/#1 & @@@ #2]], Total[Times @@@ #2]] & @@ {#, FactorInteger[#]} &, 120, 2] (* Michael De Vlieger, Jun 08 2024 *)
PROG
(PARI)
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A373480(n) = (A003415(n)%A001414(n));
CROSSREFS
Cf. A001414, A003415, A373364, A373481, A373482 (after its initial 1, positions of 0's in this sequence).
Sequence in context: A350753 A091006 A350433 * A167365 A211996 A359326
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Jun 08 2024
STATUS
approved