A112753 - OEIS

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A112753

Number of distinct prime factors of n-th number of the form 3^i*5^j.

0, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2

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OFFSET

1,5

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A001221(A003593(n)) = 2 - 0^A022336(n) + 0^A022337(n);

a(n) <= 2.

MATHEMATICA

With[{nn=120}, Take[PrimeNu/@Union[Flatten[{3^#[[1]] 5^#[[2]], 5^#[[1]] 3^#[[2]]}&/@Tuples[Range[0, nn], 2]]], nn]] (* Harvey P. Dale, Nov 29 2013 *)

CROSSREFS

Cf. A001221, A003593, A022336, A022337, A086412, A112754, A112758.