# [seqfan] Re: Analogue of A170818; Product of distinct primes of the form 6n+1 (A002476 ) dividing n.

Richard Mathar mathar at strw.leidenuniv.nl
Fri Jan 8 16:53:05 CET 2010

```Clarifying
http://list.seqfan.eu/pipermail/seqfan/2009-December/003327.html
we see that A170825(n) and A140214(n) differ at n=35, 65, 70, 77, 95, 105, 119,...:

A170825 starts

1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 11, 1, 1, 1, 5, 1, 17, 1, 1, 5, 1, 11, 23, 1, 5,
1, 1, 1, 29, 5, 1, 1, 11, 17, 5, 1, 1, 1, 1, 5, 41, 1, 1, 11, 5, 23, 47, 1,
1, 5, 17, 1, 53, 1, 55, 1, 1, 29, 59, 5, 1, 1, 1, 1, 5, 11, 1, 17, 23, 5,
71, 1, 1, 1, 5, 1, 11, 1, 1, 5, 1, 41, 83, 1, 85, 1, 29, 11, 89, 5, 1, 23,
1, 47, 5, 1, 1, 1, 11, 5, 101, 17, 1, 1, 5, 53, 107, 1, 1, 55, 1, 1, 113,
1, 115, 29, 1, 59, 17, 5

and A140214 starts

1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 11, 1, 1, 1, 5, 1, 17, 1, 1, 5, 1, 11, 23, 1, 5,
1, 1, 1, 29, 5, 1, 1, 11, 17, 175, 1, 1, 1, 1, 5, 41, 1, 1, 11, 5, 23, 47,
1, 1, 5, 17, 1, 53, 1, 55, 1, 1, 29, 59, 5, 1, 1, 1, 1, 325, 11, 1, 17, 23,
175, 71, 1, 1, 1, 5, 1, 847, 1, 1, 5, 1, 41, 83, 1, 85, 1, 29, 11, 89, 5,
1, 23, 1, 47, 475, 1, 1, 1, 11, 5, 101, 17, 1, 1, 175, 53, 107, 1, 1, 55,
1, 1, 113, 1, 115, 29, 1, 59, 2023, 5

The example of n=35: the divisors are d=1,5,7,35 and the prime
divisors are p=5,7. A170825(n)=5 (since 7 == 1 (mod 6) is excluded
and 35 is not a prime)  and A14014(n)=5*35.

Maple:

A170825 := proc(n)
a := 1 ;
for p in numtheory[factorset](n) do
if p mod 6 = 5 then
a := a*p ;
end if ;
end do ;
a ;
end proc:
seq(A170825(n),n=1..120) ;

```