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

Author

Paul D. Hanna, Jan 26 2003

Keywords

• nonn

Crossrefs

Cf. A080084, A080085, A080087.

Programs

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 *)

Formula

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