A170824 a(n) = product of distinct primes of form 6k+1 that divide n.

1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 13, 7, 1, 1, 1, 1, 19, 1, 7, 1, 1, 1, 1, 13, 1, 7, 1, 1, 31, 1, 1, 1, 7, 1, 37, 19, 13, 1, 1, 7, 43, 1, 1, 1, 1, 1, 7, 1, 1, 13, 1, 1, 1, 7, 19, 1, 1, 1, 61, 31, 7, 1, 13, 1, 67, 1, 1, 7, 1, 1, 73, 37, 1, 19, 7, 13, 79, 1, 1, 1, 1, 7, 1, 43, 1, 1, 1, 1, 91, 1, 31, 1

Offset

1,7

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Formula

a(1) = 1; for n > 1, if A020639(n) = 1 (mod 6), a(n) = A020639(n) * a(A028234(n)), otherwise a(n) = a(A028234(n)). - Antti Karttunen, Jul 09 2017

Maple

A170824 := proc(n) a := 1 ; for p in numtheory[factorset](n) do if p mod 6 = 1 then a := a*p ; end if ; end do ; a ; end proc:
A140213 := proc(n) a := 1 ; for p in numtheory[divisors](n) do if p mod 6 = 1 then a := a*p ; end if ; end do ; a ; end proc:
seq(A170824(n), n=1..120) ; # R. J. Mathar, Jan 21 2010

Mathematica

test[p_] := IntegerQ[(p - 1)/6]; a[n_]:= Module[{aux = FactorInteger[n]}, Product[If[test[aux[[i, 1]]], aux[[i, 1]], 1], {i, Length[aux]}]]; Table[a[n], {i, 1, 200}] (* Jose Grau, Feb 16 2010 *)
Table[Times@@Select[Transpose[FactorInteger[n]][[1]], IntegerQ[(#-1)/6]&], {n, 100}] (* Harvey P. Dale, Jul 29 2013 *)

Prog

(Scheme) (define (A170824 n) (if (= 1 n) n (* (if (= 1 (modulo (A020639 n) 6)) (A020639 n) 1) (A170824 (A028234 n))))) ;; Antti Karttunen, Jul 09 2017
(PARI) a(n) = my(f=factor(n)); prod(k=1, #f~, if (((p=f[k, 1])%6) == 1, p, 1)); \\ Michel Marcus, Jul 10 2017

Crossrefs

Cf. A002476, A170817.

Cf. A140213. [R. J. Mathar, Jan 21 2010]

Differs from A248909 for the first time at n=49, where a(49) = 7, while A248909(49) = 49.

Sequence in context: A339748 A325470 A240831 * A248909 A140213 A331927

Adjacent sequences: A170821 A170822 A170823 * A170825 A170826 A170827

Keyword

nonn,mult

Author

N. J. A. Sloane, Dec 25 2009, following a suggestion from Jonathan Vos Post.

Extensions

More terms from R. J. Mathar, Jan 21 2010

Status

approved