A177333 Smallest factor in the factorization of n! over distinct terms of A050376.

2, 2, 2, 2, 5, 5, 2, 2, 7, 7, 3, 3, 2, 2, 2, 2, 5, 5, 4, 3, 2, 2, 4, 4, 2, 2, 2, 2, 4, 4, 2, 2, 3, 3, 3, 3, 2, 2, 4, 4, 2, 2, 2, 2, 3, 3, 4, 4, 2, 2, 2, 2, 4, 4, 2, 2, 3, 3, 7, 7, 2, 2, 2, 2, 3, 3, 3, 4, 2, 2, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 3, 4, 2, 2, 4, 4, 5, 3, 2, 2, 4, 4, 2, 2, 2, 2, 3, 3, 2, 2, 4

Offset

2,1

References

V. S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 28-43 [Russian].

Links

Amiram Eldar, Table of n, a(n) for n = 2..1000

S. Litsyn and V. S. Shevelev, On factorization of integers with restrictions on the exponent, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A33, 1-36.

Example

The factorization of 10! = 3628800 is 2^8*3^4*5^2*7^1, where 2^8 > 3^4 > 5^2 > 7, so a(10)=7 is the smallest of these 4 factors.

Maple

A177333 := proc(n) local a, p, pow2 ; a := n! ; for p in ifactors(n!)[2] do pow2 := convert( op(2, p), base, 2) ; for j from 1 to nops(pow2) do if op(j, pow2) <> 0 then a := min(a, op(1, p)^(2^(j-1))) ; end if; end do: end do: return a ; end proc:
seq(A177333(n), n=2..120) ; # R. J. Mathar, Jun 16 2010

Mathematica

b[n_] :=2^(-1+Position[ Reverse@IntegerDigits[n, 2], _?(#==1&)])//Flatten; a[n_] := Module[{np = PrimePi[n]}, v=Table[0, {np}]; Do[p = Prime[k]; Do[v[[k]] += IntegerExponent[j, p], {j, 2, n}],  {k, 1, np}]; Min[(Prime/@Range[np])^(b/@v) // Flatten]]; Array[a, 105, 2] (* Amiram Eldar, Sep 17 2019 *)

Crossrefs

Cf. A050376, A177329, A055460, A176525, A001358, A176472, A176509, A064380, A050292.

Sequence in context: A322788 A337082 A333505 * A118486 A288026 A141299

Adjacent sequences: A177330 A177331 A177332 * A177334 A177335 A177336

Keyword

nonn

Author

Vladimir Shevelev, May 06 2010

Extensions

Corrected from a(10) on and extended beyond a(30) by R. J. Mathar, Jun 16 2010

Status

approved