A338101 Smallest odd prime dividing n is a(n)-th prime, or 0 if no such prime exists.

0, 0, 2, 0, 3, 2, 4, 0, 2, 3, 5, 2, 6, 4, 2, 0, 7, 2, 8, 3, 2, 5, 9, 2, 3, 6, 2, 4, 10, 2, 11, 0, 2, 7, 3, 2, 12, 8, 2, 3, 13, 2, 14, 5, 2, 9, 15, 2, 4, 3, 2, 6, 16, 2, 3, 4, 2, 10, 17, 2, 18, 11, 2, 0, 3, 2, 19, 7, 2, 3, 20, 2, 21, 12, 2, 8, 4, 2, 22, 3, 2, 13, 23, 2, 3, 14, 2, 5, 24, 2

Offset: 1

Author

Ilya Gutkovskiy, Nov 10 2020

Keywords

• nonn

Examples

			70 = 2 * 5 * 7 = prime(1) * prime(3) * prime(4), 3 < 4, so a(70) = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000079 (positions of 0's), A000265, A000720, A020639, A055396, A078701.

Programs

Maple

f:= proc(n) local w;
   w:= numtheory:-factorset(n) minus {2};
   if w = {} then 0 else numtheory:-pi(min(w)) fi
end proc:
map(f, [$1..100]); # Robert Israel, Nov 13 2020

Mathematica

Array[If[Or[# == 1, ! IntegerQ@ #], 0, PrimePi@ #] &@ SelectFirst[FactorInteger[#][[All, 1]], OddQ] &, 90] (* Michael De Vlieger, Nov 13 2020 *)

PARI

a(n) = my(v = select(x->((x%2)==1), factor(n)[, 1])); if (#v, primepi(vecmin(v)), 0); \\ Michel Marcus, Nov 13 2020

Formula

a(n) = A000720(A020639(A000265(n))).

a(n) = A000720(A078701(n)).