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A177334 Largest factor in the factorization of n! over distinct terms of A050376. 7
2, 3, 4, 5, 16, 16, 16, 81, 256, 256, 256, 256, 256, 256, 256, 256, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 4294967296, 4294967296, 4294967296, 4294967296, 4294967296, 4294967296 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Each number >=2 has a unique factorization over distinct terms of A050376.

This is obtained from the standard prime factor representation by splitting the exponents into a sum of powers of 2, and further factorization according to the nonzero term of this base-2 representation.

The largest factor of this representation of A000142(n) defines this sequence.

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.

MAPLE

A177334 := proc(n) local a, p, pow2 ; a := 1 ; 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 := max(a, op(1, p)^(2^(j-1))) ; end if; end do: end do: return a ; end proc:

seq(A177334(n), n=2..60) ; # 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}]; Max[(Prime/@Range[np])^(b/@v) // Flatten]]; Array[a, 38, 2]  (* Amiram Eldar, Sep 17 2019 *)

CROSSREFS

Cf. A050376, A177329, A055460, A177333, A176525, A001358, A176509, A064380, A050292.

Sequence in context: A102738 A098553 A132705 * A004834 A075687 A283526

Adjacent sequences:  A177331 A177332 A177333 * A177335 A177336 A177337

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 06 2010

EXTENSIONS

a(18) and a(19) corrected and sequence extended by R. J. Mathar, Jun 16 2010

STATUS

approved

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Last modified April 22 14:20 EDT 2021. Contains 343177 sequences. (Running on oeis4.)