|
|
A343431
|
|
Part of n composed of prime factors of the form 6k-1.
|
|
5
|
|
|
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, 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, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
Completely multiplicative with a(p) = p if p is of the form 6k-1 and a(p) = 1 otherwise.
Largest term of A259548 that divides n.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
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 *)
|
|
PROG
|
(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
(Python)
from math import prod
from sympy import factorint
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
|
|
CROSSREFS
|
Equivalent sequence for distinct prime factors: A170825.
|
|
KEYWORD
|
nonn,easy,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|