A116451 Numbers having fewer prime factors than at least one smaller number.

5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

Offset

0,1

Comments

Complement of A029744.

Numbers whose odd part is greater than 3. - Peter Munn, Aug 12 2020

Links

Table of n, a(n) for n=0..69.

Formula

A116452(n) = A001222(a(n)).

For n>=23, a(n) = n+m+2 if n+m+1>=A029744(m+1) and a(n) = n+m+1 otherwise, where m = A070939(n+1)+A070939(floor((n+1)/3)). - Chai Wah Wu, Jan 25 2026

Prog

(Python)
def A116451(n): return (5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33)[n] if n<23 else n+1+(m:=(n+1).bit_length()+((n+1)//3).bit_length())+(n+1+m>=(1<<(m+1>>1) if m&1 else 3<<(m+1>>1)-1)) # Chai Wah Wu, Jan 25 2026

Crossrefs

Cf. A029744, A116452, A001222.

Sequence in context: A354454 A194394 A160811 * A126949 A079696 A275718

Adjacent sequences: A116448 A116449 A116450 * A116452 A116453 A116454

Keyword

nonn

Author

Reinhard Zumkeller, Feb 16 2006

Extensions

The offset should really be 1, since this is a list, but that change would also require a complete rewrite of A116454, plus changes to A116453. So for the moment let's leave this with offset 0. - N. J. A. Sloane, Aug 17 2020

Status

approved