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
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