A343431 - OEIS

%I #19 Dec 29 2022 11:18:59

%S 1,1,1,1,5,1,1,1,1,5,11,1,1,1,5,1,17,1,1,5,1,11,23,1,25,1,1,1,29,5,1,

%T 1,11,17,5,1,1,1,1,5,41,1,1,11,5,23,47,1,1,25,17,1,53,1,55,1,1,29,59,

%U 5,1,1,1,1,5,11,1,17,23,5,71,1,1,1,25,1,11,1,1,5,1,41,83,1,85,1,29,11,89,5

%N Part of n composed of prime factors of the form 6k-1.

%C Completely multiplicative with a(p) = p if p is of the form 6k-1 and a(p) = 1 otherwise.

%C Largest term of A259548 that divides n.

%F a(n) = n / A065331(n) / A248909(n) = A065330(n) / A248909(n).

%t f[p_, e_] := If[Mod[p, 6] == 5, p^e, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* after _Amiram Eldar_ at A248909 *)

%o (PARI) a(n) = {my(f = factor(n)); for (i=1, #f~, if ((f[i, 1] + 1) % 6, f[i, 1] = 1); ); factorback(f); } \\ after _Michel Marcus_ at A248909

%o (Python)

%o from math import prod

%o from sympy import factorint

%o def A343431(n): return prod(p**e for p, e in factorint(n).items() if not (p+1)%6) # _Chai Wah Wu_, Dec 26 2022

%Y Equivalent sequence for distinct prime factors: A170825.

%Y Equivalent sequences for prime factors of other forms: A000265 (2k+1), A343430 (3k-1), A170818 (4k+1), A097706 (4k-1), A248909 (6k+1), A065330 (6k+/-1), A065331 (<= 3), A355582 (<= 5).

%Y Range of terms: A259548.

%K nonn,easy,mult

%O 1,5

%A _Peter Munn_, Apr 15 2021