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

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from indices in prime factorization

Formula

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

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A077962 A353484 A349134 * A338490 A213607 A298932

Adjacent sequences: A338098 A338099 A338100 * A338102 A338103 A338104

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 10 2020

Status

approved