A170817 a(n) = product of distinct primes of form 4k+1 that divide n.

1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 13, 1, 5, 1, 17, 1, 1, 5, 1, 1, 1, 1, 5, 13, 1, 1, 29, 5, 1, 1, 1, 17, 5, 1, 37, 1, 13, 5, 41, 1, 1, 1, 5, 1, 1, 1, 1, 5, 17, 13, 53, 1, 5, 1, 1, 29, 1, 5, 61, 1, 1, 1, 65, 1, 1, 17, 1, 5, 1, 1, 73, 37, 5, 1, 1, 13, 1, 5, 1, 41, 1, 1, 85, 1, 29, 1

Offset: 1

Author

N. J. A. Sloane, Dec 22 2009

Keywords

• nonn
• mult
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A170818, A170819, A097706, A083025, A170824, A170825.

Programs

Maple

a:= n-> mul (i, i=map (x-> x[1], select (x-> isprime (x[1]) and irem (x[1], 4)=1, ifactors(n)[2]))): seq (a(n), n=1..120);

Mathematica

Table[Times@@Select[Transpose[FactorInteger[n]][[1]],Mod[#,4]==1&], {n,90}] (* Harvey P. Dale, Dec 07 2012 *)

PARI

a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,1] % 4 == 1, f[i,1], 1));} \\ Amiram Eldar, Jun 09 2025

Extensions

Corrected and extended with Maple program by Alois P. Heinz, Dec 23 2009