A377985 - OEIS

%I #6 Nov 16 2024 18:48:35

%S 1,2,2,2,4,4,4,-2,-2,8,10,0,10,8,6,-22,16,-4,16,4,2,20,18,-24,8,20,

%T -46,-4,28,12,26,-98,18,32,10,-48,34,32,14,-28,40,4,40,16,-30,36,42,

%U -120,-12,16,30,8,48,-92,38,-68,26,56,58,-24,56,52,-74,-358,34,36,64,28,26,20,70,-216,68,68,-18,20,34,28

%N a(n) = 2*n - phi(A003961(n)), where phi is Euler totient function and A003961 is fully multiplicative function with a(prime(i)) = prime(i+1).

%H Antti Karttunen, <a href="/A377985/b377985.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = 2*n - A003972(n).

%F a(n) = Sum_{d|n} A008683(n/d) * A377984(d).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A377985(n) = (2*n - eulerphi(A003961(n)));

%Y Cf. A000010, A003961, A003972, A008683.

%Y Möbius transform of A377984.

%K sign

%O 1,2

%A _Antti Karttunen_, Nov 16 2024