cp's OEIS Frontend

A340073 a(n) = (x-1) / gcd(x-1, phi(x)), where x = A003961(n), i.e., n with its prime factorization shifted one step towards larger primes.

%I A340073 #6 Dec 28 2020 17:47:38
%S A340073 0,1,1,4,1,7,1,13,6,5,1,11,1,8,17,40,1,37,1,31,27,19,1,67,8,25,31,49,
%T A340073 1,13,1,121,4,14,19,28,1,17,21,47,1,41,1,29,29,43,1,101,12,73,47,19,1,
%U A340073 187,5,74,57,23,1,157,1,55,137,364,59,97,1,85,9,23,1,337,1,61,61,103,71,127,1,283,156,32,1,247,11
%N A340073 a(n) = (x-1) / gcd(x-1, phi(x)), where x = A003961(n), i.e., n with its prime factorization shifted one step towards larger primes.
%C A340073 Prime shifted analog of A160596.
%H A340073 Antti Karttunen, <a href="/A340073/b340073.txt">Table of n, a(n) for n = 1..8191</a>
%H A340073 Antti Karttunen, <a href="/A340073/a340073.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A340073 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A340073 a(n) = A160596(A003961(n)).
%F A340073 a(n) = A253885(n-1) / A340071(n) = (A003961(n)-1) / A340071(n).
%o A340073 (PARI)
%o A340073 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A340073 A340073(n) = { my(x=A003961(n)); (x-1)/gcd(x-1, eulerphi(x)); };
%Y A340073 Cf. A000010, A003961, A003972, A160596, A253885, A340071, A340072.
%Y A340073 Cf. also A340083.
%K A340073 nonn
%O A340073 1,4
%A A340073 _Antti Karttunen_, Dec 28 2020