# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a294277 Showing 1-1 of 1 %I A294277 #19 Sep 17 2024 04:03:55 %S A294277 1,5,9,11,13,17,19,23,25,27,29,32,37,41,43,47,49,53,59,61,64,65,67,69, %T A294277 71,73,77,79,81,83,89,97,101,103,104,107,109,113,119,121,125,128,129, %U A294277 131,137,139,149,151,153,155,157,163,164,167,169,173,179,181,185 %N A294277 Numbers k such that omega(k) < omega(k+1) (where omega(m) = A001221(m), the number of distinct primes dividing m). %C A294277 This sequence, alongside A006049 and A294278, form a partition of the positive integers. %C A294277 The asymptotic density of this sequence is 1/2 (Erdős, 1936). - _Amiram Eldar_, Sep 17 2024 %H A294277 Amiram Eldar, Table of n, a(n) for n = 1..10000 %H A294277 Paul Erdős, On a problem of Chowla and some related problems, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 32, No. 4 (1936), pp. 530-540; alternative link. %e A294277 omega(1) = 0 < omega(2) = 1, hence 1 belongs to this sequence. %e A294277 omega(4) = 1 = omega(5) = 1, hence 4 does not belong to this sequence. %e A294277 omega(6) = 2 > omega(7) = 1, hence 6 does not belong to this sequence. %t A294277 Position[Partition[PrimeNu[Range[200]],2,1],_?(#[[1]]<#[[2]]&),1,Heads-> False]//Flatten (* _Harvey P. Dale_, May 06 2018 *) %o A294277 (PARI) for (n=1, 185, if (omega(n) < omega(n+1), print1 (n ", "))) %Y A294277 Cf. A001221, A006049, A294278. %K A294277 nonn,easy %O A294277 1,2 %A A294277 _Rémy Sigrist_, Oct 26 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE