A339903 Fully multiplicative with a(p) = A000265(q-1), where q = A151800(p), the next prime > p.

1, 1, 1, 1, 3, 1, 5, 1, 1, 3, 3, 1, 1, 5, 3, 1, 9, 1, 11, 3, 5, 3, 7, 1, 9, 1, 1, 5, 15, 3, 9, 1, 3, 9, 15, 1, 5, 11, 1, 3, 21, 5, 23, 3, 3, 7, 13, 1, 25, 9, 9, 1, 29, 1, 9, 5, 11, 15, 15, 3, 33, 9, 5, 1, 3, 3, 35, 9, 7, 15, 9, 1, 39, 5, 9, 11, 15, 1, 41, 3, 1, 21, 11, 5, 27, 23, 15, 3, 3, 3, 5, 7, 9, 13, 33, 1, 25, 25

Offset: 1

Author

Antti Karttunen, Dec 29 2020

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000265, A003958, A003961, A005117, A151800, A339904.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A339903(n) = if(1==n,n,my(f=factor(n)); for(i=1,#f~,f[i,1] = nextprime(1+f[i,1])-1); A000265(factorback(f)));

Formula

a(n) = A336466(A003961(n)) = A000265(A003958(A003961(n))).

For all squarefree numbers k, a(k) = A339904(k).