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

Author

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

Keywords

• nonn
• mult

Links

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

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.

Programs

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 *)

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

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

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

Extensions

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