A342081 - OEIS

A342081

Numbers without an inferior odd divisor > 1.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 26, 28, 29, 31, 32, 34, 37, 38, 41, 43, 44, 46, 47, 52, 53, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 76, 79, 82, 83, 86, 88, 89, 92, 94, 97, 101, 103, 104, 106, 107, 109, 113, 116, 118, 122, 124

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OFFSET

1,2

COMMENTS

We define a divisor d|n to be inferior if d <= n/d. Inferior divisors are counted by A038548 and listed by A161906.

Numbers n such that n is either a power of 2 or has a single odd prime factor > sqrt(n). Equivalently, numbers n such that all odd prime factors are > sqrt(n). - Chai Wah Wu, Mar 08 2021

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

The divisors > 1 of 72 are {2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72}, of which {3, 9} are odd and {2, 3, 4, 6, 8} are inferior, with intersection {3}, so 72 is not in the sequence.

MATHEMATICA

Select[Range[100], Function[n, Select[Divisors[n]//Rest, OddQ[#]&&#<=n/#&]=={}]]

PROG

(Python)

from sympy import primefactors

A342081_list = [n for n in range(1, 10**3) if len([p for p in primefactors(n) if p > 2 and p*p <= n]) == 0] # Chai Wah Wu, Mar 08 2021

(PARI) is(n) = #select(x -> x > 2 && x^2 <= n, factor(n)[, 1]) == 0; \\ Amiram Eldar, Nov 01 2024

CROSSREFS

The strictly inferior version is the same with A001248 added.

Positions of 1's in A069288.

The superior version is A116882, with complement A116883.

The complement is A342082.