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A266325 Smallest integer m such that there is a partition of m with product of multiplicities of parts equal to n. 2
0, 2, 3, 4, 5, 6, 7, 8, 9, 9, 11, 10, 13, 11, 11, 12, 17, 12, 19, 13, 13, 15, 23, 14, 15, 17, 15, 15, 29, 16, 31, 16, 17, 21, 17, 17, 37, 23, 19, 18, 41, 19, 43, 19, 19, 27, 47, 20, 21, 20, 23, 21, 53, 21, 21, 21, 25, 33, 59, 22, 61, 35, 22, 22, 23, 23, 67, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..2500

FORMULA

a(n) = min { m >= 0 : A266477(m,n) > 0 }.

p in primes => a(p) = p.

MAPLE

b:= proc(n, i, p) option remember; `if`(n=0, `if`(p=1, 1, 0),

      `if`(i<1, 0, b(n, i-1, p)+add(`if`(irem(p, j)=0,

       b(n-i*j, i-1, p/j), 0), j=1..n/i)))

    end:

a:= proc(n) option remember; local m;

      if isprime(n) then return n fi;

      for m from 0 do if b(m$2, n)>0 then return m fi od

    end:

seq(a(n), n=1..100);

MATHEMATICA

b[n_, i_, p_] := b[n, i, p] = If[n == 0, If[p == 1, 1, 0], If[i < 1, 0, b[n, i - 1, p] + Sum[If[Mod[p, j] == 0, b[n - i*j, i - 1, p/j], 0], {j, 1, n/i}]]]; a[n_] := a[n] = Module[{m}, If[PrimeQ[n], Return[n]]; For[m = 0, True, m++, If[b[m, m, n] > 0, Return[m]]]]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Dec 21 2016, translated from Maple *)

CROSSREFS

Cf. A266477.

Sequence in context: A239092 A017884 A072139 * A262087 A261914 A261423

Adjacent sequences:  A266322 A266323 A266324 * A266326 A266327 A266328

KEYWORD

nonn

AUTHOR

Emeric Deutsch and Alois P. Heinz, Jan 04 2016

STATUS

approved

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Last modified September 18 13:54 EDT 2021. Contains 347527 sequences. (Running on oeis4.)