This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373362 #17 Jun 03 2024 08:54:01
%S A373362 0,1,1,2,1,1,1,3,2,7,1,1,1,1,8,4,1,1,1,1,2,1,1,1,2,1,3,1,1,1,1,5,2,1,
%T A373362 12,2,1,1,8,1,1,3,1,1,1,1,1,1,2,1,4,17,1,1,8,1,2,1,1,2,1,1,1,6,6,1,1,
%U A373362 1,2,1,1,1,1,1,1,1,6,9,1,1,4,1,1,2,2,1,8,1,1,1,20,1,2,1,12,1,1,1,1,14,1,1,1,1,1
%N A373362 a(n) = gcd(A001414(n), A276085(n)), where A001414 is the sum of prime factors with repetition, and A276085 is the primorial base log-function.
%C A373362 As A001414 and A276085 are both fully additive sequences, all sequences that give the positions of multiples of some k > 1 in this sequence are closed under multiplication: For example, A373373, which gives the indices of multiples of 3.
%H A373362 Antti Karttunen, <a href="/A373362/b373362.txt">Table of n, a(n) for n = 1..65537</a>
%o A373362 (PARI)
%o A373362 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A373362 A002110(n) = prod(i=1,n,prime(i));
%o A373362 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A373362 A373362(n) = gcd(A001414(n), A276085(n));
%Y A373362 Cf. A001414, A002110, A276085.
%Y A373362 Cf. A345452 (positions of even terms), A373373 (positions of multiples of 3).
%Y A373362 Cf. also A082299, A373361, A373363, A373367.
%K A373362 nonn
%O A373362 1,4
%A A373362 _Antti Karttunen_, Jun 02 2024