A373362 - OEIS

%I #17 Jun 03 2024 08:54:01

%S 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 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 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 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 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 Antti Karttunen, <a href="/A373362/b373362.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

%o A002110(n) = prod(i=1,n,prime(i));

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

%o A373362(n) = gcd(A001414(n), A276085(n));

%Y Cf. A001414, A002110, A276085.

%Y Cf. A345452 (positions of even terms), A373373 (positions of multiples of 3).

%Y Cf. also A082299, A373361, A373363, A373367.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jun 02 2024