%I #12 Dec 29 2020 20:37:49

%S 1,1,1,3,3,1,5,9,5,3,3,3,1,5,3,27,9,5,11,9,5,3,7,9,21,1,25,15,15,3,9,

%T 81,3,9,15,15,5,11,1,27,21,5,23,9,15,7,13,27,55,21,9,3,29,25,9,45,11,

%U 15,15,9,33,9,25,243,3,3,35,27,7,15,9,45,39,5,21,33,15,1,41,81,125,21,11,15,27,23,15,27,3,15

%N The odd part of {Euler totient function phi applied to the prime shifted n}: a(n) = A000265(A000010(A003961(n))).

%H Antti Karttunen, <a href="/A339904/b339904.txt">Table of n, a(n) for n = 1..8191</a>

%H Antti Karttunen, <a href="/A339904/a339904.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

%F Multiplicative with a(p^e) = A000265(q-1) * q^(e-1), where q = A151800(p), the next prime larger than p.

%F a(n) = A000265(A003972(n)) = A053575(A003961(n)) = A000265(A000010(A003961(n))).

%F For all squarefree numbers k, a(k) = A339903(k).

%o (PARI)

%o A000265(n) = (n>>valuation(n,2));

%o A339904(n) = if(1==n,n,my(f=factor(n)); prod(i=1,#f~,my(q=nextprime(1+f[i,1])); A000265(q-1)*(q^(f[i,2]-1))));

%o (PARI)

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

%o A339903(n) = A000265(eulerphi(A003961(n)));

%Y Cf. A000010, A000265, A003961, A003972, A005117, A053575, A151800, A339903, A340075.

%K nonn,mult

%O 1,4

%A _Antti Karttunen_, Dec 29 2020