A036347 - OEIS

%I #21 Jan 16 2023 11:16:15

%S 1,6,9,10,12,14,15,20,21,22,24,25,26,28,33,34,35,38,39,40,44,46,48,49,

%T 51,52,54,55,56,57,58,62,65,68,69,74,76,77,80,81,82,85,86,87,88,90,91,

%U 92,93,94,95,96,104,106,108,111,112,115,116,118,119,121,122,123,124,126,129,133,134,135,136

%N Numbers k for which the parity of k and the parity of sopfr(k) differ, where sopfr is the sum of prime factors with repetition.

%C Parity of n and its sum of prime factors differs (counted with multiplicity). - The original name.

%H Antti Karttunen, <a href="/A036347/b036347.txt">Table of n, a(n) for n = 1..10000</a>

%F {k | k+A001414(k) == 1 mod 2}. - _Antti Karttunen_, Jan 16 2023

%e 111 = 3 * 37 -> sum = 40 so 111 is odd while 40 is even.

%o (PARI) isA036347(n) = A359768(n); \\ _Antti Karttunen_, Jan 15 2023

%o (Python)

%o from itertools import count, islice

%o from functools import reduce

%o from operator import ixor

%o from sympy import factorint

%o def A036347_gen(startvalue=1): # generator of terms

%o     return filter(lambda n:(reduce(ixor,(p*e for p, e in factorint(n).items()),0)^n)&1, count(max(startvalue,1)))

%o A036347_list = list(islice(A036347_gen(),20)) # _Chai Wah Wu_, Jan 15 2023

%Y Cf. A001414, A030141, A359768 (characteristic function).

%Y Union of A036348 (even terms) and A046337 (odd terms).

%Y Positions of odd terms in A075254 and in A075255.

%Y Cf. also A359771, A359821.

%K nonn,base

%O 1,2

%A _Patrick De Geest_, Dec 15 1998

%E Missing initial term a(1) = 1 prepended, offset corrected, name edited and more terms added by _Antti Karttunen_, Jan 15 2023