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

6, 10, 12, 14, 20, 22, 24, 26, 28, 34, 38, 40, 44, 46, 48, 52, 54, 56, 58, 62, 68, 74, 76, 80, 82, 86, 88, 90, 92, 94, 96, 104, 106, 108, 112, 116, 118, 122, 124, 126, 134, 136, 142, 146, 148, 150, 152, 158, 160, 164, 166, 172, 176, 178, 180, 184, 188, 192, 194, 198, 202, 206, 208

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• base

Comments

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

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

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Even terms in A036347 and in A335657.

Setwise difference A036347 \ A046337.

Setwise difference A335657 \ A067019.

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

Programs

Mathematica

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

PARI

isA036348(n) = (!(n%2) && (bigomega(n>>valuation(n,2))%2)); \\ Antti Karttunen, Jan 15 2023

Formula

{k | k == 0 mod 2 and A087436(n) == 1 mod 2}. - Antti Karttunen, Jan 16 2023

Extensions

Offset corrected, name edited and more terms added by Antti Karttunen, Jan 15 2023