A173345 Number of trailing zeros of the superfactorial of n (A000178).

0, 0, 0, 0, 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 34, 38, 42, 46, 50, 56, 62, 68, 74, 80, 87, 94, 101, 108, 115, 123, 131, 139, 147, 155, 164, 173, 182, 191, 200, 210, 220, 230, 240, 250, 262, 274, 286, 298, 310, 323, 336, 349, 362, 375, 389, 403, 417

Offset: 1

Author

José María Grau Ribas, Feb 16 2010

Keywords

• easy
• base
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• A. M. Oller-Marcen and J. Maria Grau, On the Base-b Expansion of the Number of Trailing Zeros of b^k!, J. Int. Seq. 14 (2011), Article 11.6.8.
• Eric Weisstein's World of Mathematics, Superfactorial.

Crossrefs

Cf. A000178, A027868.

Programs

Mathematica

a[n_] := Sum[Z10[i], {i, n}]; Z10[n_]:= Floor[Sum[Floor[n/5^i], {i, 1, Floor[Log[5, n]]}]]; Join[{0},Table[a[n], {n, 2, 200}]]
a[0] := 1; a[1] := 1; a[n_] := n!*a[n - 1];IntegerExponent[Table[a[n], {n, 1, 100}]] (* Stefano Spezia, Jan 26 2023 *)

PARI

a(n)=my(t=0);sum(k=5,n,t+=valuation(k,5)) \\ Charles R Greathouse IV, Jun 10 2011

Formula

a(n) = Sum_{k=1..n} A027868(k). - Charles R Greathouse IV, Jun 10 2011