A340071 - OEIS

%I #8 Dec 28 2020 17:47:24

%S 1,2,4,2,6,2,10,2,4,4,12,4,16,4,2,2,18,2,22,2,2,2,28,2,6,2,4,2,30,8,

%T 36,2,16,4,4,8,40,4,4,4,42,4,46,4,6,2,52,4,10,2,2,8,58,2,18,4,2,4,60,

%U 2,66,2,2,2,2,2,70,2,16,10,72,2,78,2,4,2,2,2,82,2,4,4,88,2,12,4,2,2,96,4,2,4,8,2,4,2,100

%N a(n) = gcd(A003961(n)-1, phi(A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes.

%C Prime shifted analog of A049559.

%H Antti Karttunen, <a href="/A340071/b340071.txt">Table of n, a(n) for n = 1..65537</a>

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

%F a(n) = A049559(A003961(n)).

%F a(n) = gcd(A253885(n-1), A003972(n)) = gcd(A003961(n)-1, A000010(A003961(n))).

%F a(n) = A003972(n) / A340072(n).

%F For n > 1, a(n) = (A003961(n)-1) / A340073(n).

%o (PARI)

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

%o A340071(n) = { my(u=A003961(n)); gcd(u-1, eulerphi(u)); };

%Y Cf. A000010, A003961, A003972, A049559, A253885, A340072, A340073.

%Y Cf. also A340081.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 28 2020