A036348 - OEIS

%I #35 Jan 16 2023 11:15:40

%S 6,10,12,14,20,22,24,26,28,34,38,40,44,46,48,52,54,56,58,62,68,74,76,

%T 80,82,86,88,90,92,94,96,104,106,108,112,116,118,122,124,126,134,136,

%U 142,146,148,150,152,158,160,164,166,172,176,178,180,184,188,192,194,198,202,206,208

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

%C Parity of 'even number' and its sum of prime factors differs (counted with multiplicity). - The original name of the sequence.

%C 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 Antti Karttunen, <a href="/A036348/b036348.txt">Table of n, a(n) for n = 1..10000</a>

%F {k | k == 0 mod 2 and A087436(n) == 1 mod 2}. - _Antti Karttunen_, Jan 16 2023

%e 88 = 2 * 2 * 2 * 11 -> sum = 17; 88 is even while 17 is odd, so 88 is a term.

%t Select[2*Range[100],OddQ[Total[Flatten[Table[#[[1]],{#[[2]]}]&/@ FactorInteger[#]]]]&] (* _Harvey P. Dale_, Sep 22 2014 *)

%o (PARI) isA036348(n) = (!(n%2) && (bigomega(n>>valuation(n,2))%2)); \\ _Antti Karttunen_, Jan 15 2023

%Y Even terms in A036347 and in A335657.

%Y Setwise difference A036347 \ A046337.

%Y Setwise difference A335657 \ A067019.

%Y Cf. A000079, A000265, A001222, A036349, A046470, A087436.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Dec 15 1998

%E Offset corrected, name edited and more terms added by _Antti Karttunen_, Jan 15 2023