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

1,1

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Even terms in A036347 and in A335657.

Setwise difference A036347 \ A046337.

Setwise difference A335657 \ A067019.

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

Sequence in context: A036350 A295076 A088829 * A100368 A128691 A359875

Adjacent sequences: A036345 A036346 A036347 * A036349 A036350 A036351

Keyword

nonn,base

Author

Patrick De Geest, Dec 15 1998

Extensions

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

Status

approved