A359587 Fully multiplicative with a(p) = A008578(1+A329697(p)).

1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 3, 2, 3, 3, 4, 1, 2, 4, 5, 2, 6, 3, 5, 2, 4, 3, 8, 3, 5, 4, 5, 1, 6, 2, 6, 4, 5, 5, 6, 2, 3, 6, 7, 3, 8, 5, 7, 2, 9, 4, 4, 3, 5, 8, 6, 3, 10, 5, 7, 4, 5, 5, 12, 1, 6, 6, 7, 2, 10, 6, 7, 4, 5, 5, 8, 5, 9, 6, 7, 2, 16, 3, 5, 6, 4, 7, 10, 3, 5, 8, 9, 5, 10, 7, 10, 2, 3, 9, 12, 4, 5, 4, 5, 3, 12

Offset: 1

Author

Antti Karttunen, Jan 08 2023

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000265, A001222, A008578, A056239, A087436, A318995, A329697, A336396, A336466.

Programs

PARI

A008578(n) = if(1==n,1,prime(n-1));
A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A359587(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 1] = A008578(1+A329697(f[i, 1]))); factorback(f); };

Formula

For n >= 1: (Start)

a(A000265(n)) = a(2*n) = a(n).

A001222(a(n)) = A087436(n),

A056239(a(n)) = A329697(n),

A318995(a(n)) = A336396(n) = A329697(A336466(n)).

(End)