A170818 a(n) is the product of primes (with multiplicity) of form 4*k+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, 25, 13, 1, 1, 29, 5, 1, 1, 1, 17, 5, 1, 37, 1, 13, 5, 41, 1, 1, 1, 5, 1, 1, 1, 1, 25, 17, 13, 53, 1, 5, 1, 1, 29, 1, 5, 61, 1, 1, 1, 65, 1, 1, 17, 1, 5, 1, 1, 73, 37, 25, 1, 1, 13, 1, 5, 1, 41, 1, 1, 85, 1, 29, 1

Offset

1,5

Comments

Completely multiplicative with a(p) = p if p = 4k+1 and a(p) = 1 otherwise. - Tom Edgar, Mar 05 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

A. Tripathi, On Pythagorean triples containing a fixed integer, Fib. Q., 46/47 (2008/2009), 331-340.

Index to divisibility sequences

Formula

a(n) = n/A072438(n). - Michel Marcus, Mar 05 2015

Maple

a:= n-> mul(`if`(irem(i[1], 4)=1, i[1]^i[2], 1), i=ifactors(n)[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 09 2014

Mathematica

a[n_] := Product[{p, e} = pe; If[Mod[p, 4] == 1, p^e, 1], {pe, FactorInteger[n]}];
Array[a, 100] (* Jean-François Alcover, May 29 2019 *)

Prog

(PARI) a(n)=my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, f[i, 1])^f[i, 2]) \\ Charles R Greathouse IV, Jun 28 2015
(Python)
from sympy import factorint, prod
def a072438(n):
    f = factorint(n)
    return 1 if n == 1 else prod(i**f[i] for i in f if i % 4 != 1)
def a(n): return n//a072438(n) # Indranil Ghosh, May 08 2017

Crossrefs

Cf. A170817-A170819, A097706, A083025, A072438, A286361.

Sequence in context: A135469 A348735 A170817 * A046622 A170825 A140214

Adjacent sequences: A170815 A170816 A170817 * A170819 A170820 A170821

Keyword

nonn,mult

Author

N. J. A. Sloane, Dec 22 2009

Status

approved