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After 1, numbers k > 1 such that k has fewer prime divisors than k-1, when they are counted with multiplicity.
5

%I #18 May 15 2023 08:44:27

%S 1,5,7,9,11,13,17,19,21,23,25,29,31,33,37,41,43,46,47,49,51,53,55,57,

%T 59,61,65,67,69,71,73,77,79,81,82,83,85,89,91,93,97,101,103,105,106,

%U 107,109,111,113,115,118,121,127,129,131,133,137,139,141,145,149,151,153,155,157,161,163,166,167,169,173,177,179

%N After 1, numbers k > 1 such that k has fewer prime divisors than k-1, when they are counted with multiplicity.

%C List of starts of nondecreasing runs of values of A001222 (= bigomega, number of prime factors, when counted with multiplicity).

%C Differs from A303578 (a similar sequence computed for tau, the number of divisors) for the first time at n=44, where a(44) = 105, a term missing from A303578.

%H Antti Karttunen, <a href="/A339910/b339910.txt">Table of n, a(n) for n = 1..28208; all terms <= 65537</a>

%t 1 + {0}~Join~Position[Sign@ Differences[Array[PrimeOmega, 180]], -1][[All, 1]] (* _Michael De Vlieger_, Dec 22 2020 *)

%o (PARI) isA339910(n) = ((1==n)||(bigomega(n)<bigomega(n-1)));

%Y Cf. A001222.

%Y One more than A322839.

%Y Cf. A339911, A339912 for subsequences.

%Y Cf. also A303578.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 22 2020