cp's OEIS Frontend

A373363 a(n) = gcd(A001414(n), A083345(n)), where A001414 is the sum of prime factors with repetition, and A083345 is the numerator of the sum of the inverses of prime factors with repetition.

%I A373363 #8 Jun 02 2024 17:34:36
%S A373363 0,1,1,1,1,5,1,3,2,7,1,1,1,9,8,2,1,1,1,3,10,13,1,1,2,15,1,1,1,1,1,5,
%T A373363 14,19,12,5,1,21,16,1,1,1,1,3,1,25,1,1,2,3,20,1,1,1,16,1,22,31,1,1,1,
%U A373363 33,1,3,18,1,1,3,26,1,1,1,1,39,1,1,18,1,1,1,4,43,1,1,22,45,32,1,1,1,20,3,34,49,24,1,1,1,1,7
%N A373363 a(n) = gcd(A001414(n), A083345(n)), where A001414 is the sum of prime factors with repetition, and A083345 is the numerator of the sum of the inverses of prime factors with repetition.
%H A373363 Antti Karttunen, <a href="/A373363/b373363.txt">Table of n, a(n) for n = 1..65537</a>
%o A373363 (PARI)
%o A373363 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A373363 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A373363 A373363(n) = gcd(A001414(n), A083345(n));
%Y A373363 Cf. A001414, A083345.
%Y A373363 Cf. A345452 (positions of even terms), A353374 (their characteristic function).
%Y A373363 Cf. also A082299, A373362.
%K A373363 nonn
%O A373363 1,6
%A A373363 _Antti Karttunen_, Jun 02 2024