cp's OEIS Frontend

A036347 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.

%I A036347 #21 Jan 16 2023 11:16:15
%S A036347 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 A036347 51,52,54,55,56,57,58,62,65,68,69,74,76,77,80,81,82,85,86,87,88,90,91,
%U A036347 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 A036347 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 A036347 Parity of n and its sum of prime factors differs (counted with multiplicity). - The original name.
%H A036347 Antti Karttunen, <a href="/A036347/b036347.txt">Table of n, a(n) for n = 1..10000</a>
%F A036347 {k | k+A001414(k) == 1 mod 2}. - _Antti Karttunen_, Jan 16 2023
%e A036347 111 = 3 * 37 -> sum = 40 so 111 is odd while 40 is even.
%o A036347 (PARI) isA036347(n) = A359768(n); \\ _Antti Karttunen_, Jan 15 2023
%o A036347 (Python)
%o A036347 from itertools import count, islice
%o A036347 from functools import reduce
%o A036347 from operator import ixor
%o A036347 from sympy import factorint
%o A036347 def A036347_gen(startvalue=1): # generator of terms
%o A036347     return filter(lambda n:(reduce(ixor,(p*e for p, e in factorint(n).items()),0)^n)&1, count(max(startvalue,1)))
%o A036347 A036347_list = list(islice(A036347_gen(),20)) # _Chai Wah Wu_, Jan 15 2023
%Y A036347 Cf. A001414, A030141, A359768 (characteristic function).
%Y A036347 Union of A036348 (even terms) and A046337 (odd terms).
%Y A036347 Positions of odd terms in A075254 and in A075255.
%Y A036347 Cf. also A359771, A359821.
%K A036347 nonn,base
%O A036347 1,2
%A A036347 _Patrick De Geest_, Dec 15 1998
%E A036347 Missing initial term a(1) = 1 prepended, offset corrected, name edited and more terms added by _Antti Karttunen_, Jan 15 2023