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A286582 a(n) = A001222(A048673(n)). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

FORMULA

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

PROG

(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));

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

(Python)

from sympy import factorint, nextprime, primefactors

from operator import mul

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 + reduce(mul, [nextprime(i)**f[i] for i in f]))/2

def a(n): return a001222(a048673(n))

print [a(n) for n in range(1, 101)] # Indranil Ghosh, Jun 12 2017

CROSSREFS

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

Sequence in context: A323326 A274884 A076224 * A114729 A186037 A144365

Adjacent sequences:  A286579 A286580 A286581 * A286583 A286584 A286585

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 31 2017

STATUS

approved

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)