cp's OEIS Frontend

A036348 Even numbers whose number of odd prime factors is odd (when counted with multiplicity).

%I A036348 #35 Jan 16 2023 11:15:40
%S A036348 6,10,12,14,20,22,24,26,28,34,38,40,44,46,48,52,54,56,58,62,68,74,76,
%T A036348 80,82,86,88,90,92,94,96,104,106,108,112,116,118,122,124,126,134,136,
%U A036348 142,146,148,150,152,158,160,164,166,172,176,178,180,184,188,192,194,198,202,206,208
%N A036348 Even numbers whose number of odd prime factors is odd (when counted with multiplicity).
%C A036348 Parity of 'even number' and its sum of prime factors differs (counted with multiplicity). - The original name of the sequence.
%C A036348 Even terms of A036347, and even terms of A335657. Term is listed if and only if it is the product of a term of A067019 and a power of 2 (term of A000079) larger than 1. Cf. also A036349. - _Antti Karttunen_, Jan 15 2023
%H A036348 Antti Karttunen, <a href="/A036348/b036348.txt">Table of n, a(n) for n = 1..10000</a>
%F A036348 {k | k == 0 mod 2 and A087436(n) == 1 mod 2}. - _Antti Karttunen_, Jan 16 2023
%e A036348 88 = 2 * 2 * 2 * 11 -> sum = 17; 88 is even while 17 is odd, so 88 is a term.
%t A036348 Select[2*Range[100],OddQ[Total[Flatten[Table[#[[1]],{#[[2]]}]&/@ FactorInteger[#]]]]&] (* _Harvey P. Dale_, Sep 22 2014 *)
%o A036348 (PARI) isA036348(n) = (!(n%2) && (bigomega(n>>valuation(n,2))%2)); \\ _Antti Karttunen_, Jan 15 2023
%Y A036348 Even terms in A036347 and in A335657.
%Y A036348 Setwise difference A036347 \ A046337.
%Y A036348 Setwise difference A335657 \ A067019.
%Y A036348 Cf. A000079, A000265, A001222, A036349, A046470, A087436.
%K A036348 nonn,base
%O A036348 1,1
%A A036348 _Patrick De Geest_, Dec 15 1998
%E A036348 Offset corrected, name edited and more terms added by _Antti Karttunen_, Jan 15 2023