A286582 a(n) = A001222(A048673(n)).

0, 1, 1, 1, 2, 3, 2, 2, 1, 1, 1, 1, 2, 1, 3, 1, 2, 2, 3, 5, 3, 3, 2, 3, 2, 2, 3, 3, 4, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 4, 1, 4, 3, 3, 2, 1, 2, 5, 2, 3, 3, 2, 1, 2, 1, 1, 2, 2, 4, 3, 2, 4, 3, 4, 2, 1, 3, 1, 3, 4, 2, 2, 4, 5, 7, 3, 3, 1, 2, 3, 4, 1, 1, 3, 5, 2, 1, 2, 1, 2, 5, 4, 6, 2, 3, 1, 2, 3, 2, 4, 3, 1, 1

Offset: 1

Author

Antti Karttunen, May 31 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A048673, A091304, A278224, A286583, A286584, A286585.

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A048673(n) = (A003961(n)+1)/2;
A286582(n) = bigomega(A048673(n));

Python

from sympy import factorint, nextprime, primefactors, prod
def a001222(n): return 0 if n==1 else a001222(n//primefactors(n)[-1]) + 1
def a048673(n):
    f = factorint(n)
    return 1 if n==1 else (1 + prod(nextprime(i)**f[i] for i in f))//2
def a(n): return a001222(a048673(n))
print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Jun 12 2017

Scheme

(define (A286582 n) (A001222 (A048673 n)))

Formula

a(n) = A001222(A048673(n)).