A078701 Least odd prime factor of n, or 1 if no such factor exists.

1, 1, 3, 1, 5, 3, 7, 1, 3, 5, 11, 3, 13, 7, 3, 1, 17, 3, 19, 5, 3, 11, 23, 3, 5, 13, 3, 7, 29, 3, 31, 1, 3, 17, 5, 3, 37, 19, 3, 5, 41, 3, 43, 11, 3, 23, 47, 3, 7, 5, 3, 13, 53, 3, 5, 7, 3, 29, 59, 3, 61, 31, 3, 1, 5, 3, 67, 17, 3, 5, 71, 3, 73, 37, 3, 19, 7, 3, 79, 5, 3, 41, 83, 3, 5, 43, 3, 11

Offset: 1

Author

Reinhard Zumkeller, Dec 18 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A000265, A020639, A005408, A000079.

Programs

Haskell

a078701 n = if null odds then 1 else head odds
            where odds = tail $ a182469_row n
-- Reinhard Zumkeller, Oct 08 2012

Maple

A078701 := proc(n)
    fs := numtheory[factorset](n) minus {2};
    if fs = {} then
        1;
    else
        min(op(fs)) ;
    end if;
end proc: # R. J. Mathar, Feb 06 2019

Mathematica

lof[n_]:=Module[{fac=Select[Transpose[FactorInteger[n]][[1]],OddQ]}, If[fac=={},1,Min[fac]]]; Array[lof,90] (* Harvey P. Dale, Apr 14 2012 *)
a[n_] := FactorInteger[n/2^IntegerExponent[n, 2]][[1, 1]]; Array[a, 100] (* Amiram Eldar, Jul 04 2022 *)

PARI

a(n) = my(v = select(x->((x%2)==1), factor(n)[,1])); if (#v, vecmin(v), 1); \\ Michel Marcus, Oct 25 2017

PARI

A078701(n)=iferr(factor(n)[2-bittest(n,0),1],E,1) \\ M. F. Hasler, Nov 06 2017

Python

from sympy import factorint
def A078701(n): return min((p for p in factorint(n) if p > 2), default=1) # Chai Wah Wu, Feb 03 2022

Formula

a(n) = A020639(A000265(n));

a(n) = A020639(n) iff n is odd; a(2^k) = 1.