A373365 - OEIS

%I #8 Jun 03 2024 00:27:10

%S 0,1,1,2,1,1,1,3,2,1,1,1,1,1,1,4,1,1,1,1,2,1,1,1,2,3,3,1,1,2,1,5,7,1,

%T 1,2,1,7,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,8,1,2,1,1,1,1,1,1,6,2,8,1,7,

%U 1,2,1,1,1,1,1,1,9,2,1,1,4,1,1,2,2,9,1,1,1,1,1,9,1,1,3,1,1,1,1,2,1,2,1,1,3

%N a(n) = gcd(A001414(n), A064097(n)), where A001414 is the sum of prime factors with repetition, and A064097 is a quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1.

%C As A001414 and A064097 are both fully additive sequences, all sequences that give the positions of multiples of some k > 1 in this sequence are closed under multiplication.

%H Antti Karttunen, <a href="/A373365/b373365.txt">Table of n, a(n) for n = 1..100000</a>

%o (PARI)

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

%o A064097(n) = if(1==n,0,1+A064097(n-(n/vecmin(factor(n)[,1]))));

%o A373365(n) = gcd(A001414(n), A064097(n));

%Y Cf. A001414, A064097.

%Y Cf. also A082299, A373362, A373363, A373364, A373366.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jun 02 2024