A347826 Numbers k with at least one odd semiprime divisor < k.

18, 27, 30, 36, 42, 45, 50, 54, 60, 63, 66, 70, 72, 75, 78, 81, 84, 90, 98, 99, 100, 102, 105, 108, 110, 114, 117, 120, 125, 126, 130, 132, 135, 138, 140, 144, 147, 150, 153, 154, 156, 162, 165, 168, 170, 171, 174, 175, 180, 182, 186, 189, 190, 195, 196, 198, 200, 204, 207

Offset

1,1

Comments

Also, numbers with at least 1 partition into two parts (s,t), s<=t, such that s is an odd semiprime divisor of t.

Links

Table of n, a(n) for n=1..59.

Eric Weisstein's World of Mathematics, Proper divisors

Eric Weisstein's World of Mathematics, Semiprime

Example

18 is in the sequence since 9 | 18, and 9 is an odd semiprime < n.
30 is in the sequence since 15 | 30, and 15 is an odd semiprime < n.

Mathematica

q[n_] := If[EvenQ[n], PrimeOmega[n/2^IntegerExponent[n, 2]] > 1, PrimeOmega[n] > 2]; Select[Range[200], q] (* Amiram Eldar, Jan 23 2022 *)

Prog

(PARI) isok(m) = sumdiv(m, d, if ((d<m) && (d%2), bigomega(d)==2)) > 0; \\ Michel Marcus, Jan 23 2022

Crossrefs

Cf. A001358 (semiprimes), A032741, A086971.

Sequence in context: A338385 A220100 A080910 * A036763 A226971 A281918

Adjacent sequences: A347823 A347824 A347825 * A347827 A347828 A347829

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 23 2022

Status

approved