A080086 Number of factors of 3 in the factorial of the n-th prime, counted with multiplicity.

0, 1, 1, 2, 4, 5, 6, 8, 9, 13, 14, 17, 18, 19, 21, 23, 27, 28, 31, 32, 34, 36, 40, 42, 46, 48, 49, 50, 53, 54, 61, 62, 66, 67, 71, 72, 75, 80, 81, 84, 86, 88, 93, 94, 95, 97, 102, 108, 110, 111, 112, 115, 116, 123, 126, 129, 131, 134, 136, 138, 139, 143, 151, 152, 153

Offset

1,4

Links

Table of n, a(n) for n=1..65.

Formula

a(n) = sum_{k=1..L} floor(prime(n) / 3^k), where L = log(p_n)/log(3).

Mathematica

lst={}; Do[p=Prime[n]; s=0; While[p>1, p=IntegerPart[p/3]; s+=p; ]; AppendTo[lst, s], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 28 2009 *)
Join[{0}, FactorInteger[#][[2, 2]]&/@(Prime[Range[2, 70]]!)] (* Harvey P. Dale, Sep 05 2014 *)

Crossrefs

Cf. A080084, A080085, A080087.

Sequence in context: A233564 A333222 A030326 * A229133 A015844 A114318

Adjacent sequences: A080083 A080084 A080085 * A080087 A080088 A080089

Keyword

nonn

Author

Paul D. Hanna, Jan 26 2003

Status

approved