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

1,3

Links

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

Formula

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

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

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 *)

Prog

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

Crossrefs

Cf. A000265, A020639, A005408, A000079.

Sequence in context: A308655 A356365 A217663 * A299766 A161398 A204455

Adjacent sequences: A078698 A078699 A078700 * A078702 A078703 A078704

Keyword

nonn

Author

Reinhard Zumkeller, Dec 18 2002

Status

approved