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A051703 Maximal value of products of partitions of n into powers of distinct primes (1 not considered a power). 6
1, 0, 2, 3, 4, 6, 0, 12, 15, 20, 30, 28, 60, 40, 84, 105, 140, 210, 180, 420, 280, 330, 360, 840, 504, 1260, 1155, 1540, 2310, 2520, 4620, 3080, 5460, 3960, 9240, 5544, 13860, 6552, 16380, 15015, 27720, 30030, 32760, 60060, 40040, 45045, 51480, 120120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert Gerbicz, Table of n, a(n) for n = 0..1000

J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202-209.

EXAMPLE

a(11) = 28 because max{11, 2*3^2, 2^3*3, 2^2*7} = 28.

MAPLE

b:= proc(n, i) option remember; local p;

      p:= `if`(i<1, 1, ithprime(i));

      `if`(n=0, 1, `if`(i<1 or n<0, 0, max(b(n, i-1),

      seq(p^j*b(n-p^j, i-1), j=1..ilog[p](n))) ))

    end:

a:= n-> b(n, numtheory[pi](n)):

seq(a(n), n=0..60);  # Alois P. Heinz, Feb 16 2013

MATHEMATICA

nmax = 48; Do[a[n]=0, {n, 1, nmax}]; km = PrimePi[nmax]; For[k=1, k <= km, k++, q = 1; p = Prime[k]; For[i=nmax, i >= 1, i--, q=1; While[q*p <= i, q *= p; If[i == q, m = q, If[a[i - q] != 0, m = q*a[i - q], m = 0]]; a[i] = Max[a[i], m]]]]; a[0] = 1; Table[a[n], {n, 0, nmax}] (* Jean-Fran├žois Alcover, Aug 02 2012, translated from Robert Gerbicz's Pari program *)

PROG

(PARI) {N=1000; v=vector(N, i, 0); forprime(p=2, N, q=1; forstep(i=N, 1, -1,

q=1; while(q*p<=i, q*=p; if(i==q, M=q, if(v[i-q], M=q*v[i-q], M=0));

v[i]=max(v[i], M)))); print(0" "1); for(i=1, N, print(i" "v[i]))} \\ Robert Gerbicz, Jul 31 2012

CROSSREFS

Largest element of n-th row of A080743.

A000793(n)=max{A000793(n-1), a(n)}, A000793(0)=1.

Cf. A008475, A051613, A080743, A080744, A051704.

Sequence in context: A038106 A046942 A307257 * A004567 A030378 A280244

Adjacent sequences:  A051700 A051701 A051702 * A051704 A051705 A051706

KEYWORD

nonn

AUTHOR

Vladeta Jovovic

EXTENSIONS

Corrected and extended by Robert Gerbicz, Jul 31 2012

STATUS

approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)