A365605 - OEIS

A365605

Characteristic function of numbers without an inferior odd divisor > 1.

1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0

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OFFSET

COMMENTS

We define a divisor d|n to be inferior if d*d <= n.

LINKS

Christian Krause, Table of n, a(n) for n = 1..10000

FORMULA

a(p) = 1, for p prime.

EXAMPLE

The divisors > 1 of 14 are {2, 7, 14} of which {2, 14} are even and 7 is not inferior, hence a(14)=1.

The divisors > 1 of 15 are {3, 5, 15} of which 3 is odd and inferior, hence a(15)=0.

MATHEMATICA

a[n_]:=If[Select[Divisors[n]//Rest, OddQ[#]&&#<=n/#&]=={}, 1, 0]; Array[a, 100] (* Stefano Spezia, Sep 13 2023 after Gus Wiseman in A342081 *)

PROG

(PARI) a(n) = { my(P=factor(n)[, 1]); sum(i=1, #P, P[i]>2 && P[i]*P[i]<=n)==0 }

(PARI) a(n) = sumdiv(n, d, if ((d%2) && (d>1), d^2 <= n)) == 0; \\ Michel Marcus, Sep 14 2023

CROSSREFS

Characteristic function of A342081.

Sequence in context: A328306 A267256 A351824 * A365716 A334460 A071023

Adjacent sequences: A365602 A365603 A365604 * A365606 A365607 A365608

KEYWORD

nonn

AUTHOR

Christian Krause, Sep 11 2023

STATUS

approved