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A294277 Numbers k such that omega(k) < omega(k+1) (where omega(m) = A001221(m), the number of distinct primes dividing m). 8
1, 5, 9, 11, 13, 17, 19, 23, 25, 27, 29, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 65, 67, 69, 71, 73, 77, 79, 81, 83, 89, 97, 101, 103, 104, 107, 109, 113, 119, 121, 125, 128, 129, 131, 137, 139, 149, 151, 153, 155, 157, 163, 164, 167, 169, 173, 179, 181, 185 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence, alongside A006049 and A294278, form a partition of the positive integers.

LINKS

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

EXAMPLE

omega(1) = 0 < omega(2) = 1, hence 1 belongs to this sequence.

omega(4) = 1 = omega(5) = 1, hence 4 does not belong to this sequence.

omega(6) = 2 > omega(7) = 1, hence 6 does not belong to this sequence.

MATHEMATICA

Position[Partition[PrimeNu[Range[200]], 2, 1], _?(#[[1]]<#[[2]]&), 1, Heads-> False]//Flatten (* Harvey P. Dale, May 06 2018 *)

PROG

(PARI) for (n=1, 185, if (omega(n) < omega(n+1), print1 (n ", ")))

CROSSREFS

Cf. A001221, A006049, A294278.

Sequence in context: A314584 A335486 A347771 * A043721 A043727 A043731

Adjacent sequences:  A294274 A294275 A294276 * A294278 A294279 A294280

KEYWORD

nonn,easy

AUTHOR

Rémy Sigrist, Oct 26 2017

STATUS

approved

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Last modified October 18 03:25 EDT 2021. Contains 348065 sequences. (Running on oeis4.)