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A177333 Smallest factor in the factorization of n! over distinct terms of A050376. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A181058 A301452 A322788 * 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

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Last modified December 10 20:23 EST 2019. Contains 329909 sequences. (Running on oeis4.)