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A128630 Let gpf(1)=1 and gpf(n)=greatest prime factor of n, n>1. Then a(n)=minimum sum of gpf of the parts of a partition of n. 2
0, 1, 2, 3, 2, 3, 3, 4, 2, 3, 4, 5, 3, 4, 5, 5, 2, 3, 3, 4, 4, 5, 5, 6, 3, 4, 5, 3, 4, 5, 5, 5, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 5, 5, 5, 6, 7, 3, 4, 5, 6, 5, 6, 3, 4, 5, 6, 5, 5, 5, 6, 5, 6, 2, 3, 4, 5, 4, 5, 5, 6, 3, 4, 5, 5, 5, 6, 6, 7, 4, 3, 4, 5, 6, 5, 5, 6, 5, 5, 5, 5, 6, 6, 7, 7, 3, 4, 5, 6, 5, 6, 6, 7, 5, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Reinhard Zumkeller and Alois P. Heinz, Table of n, a(n) for n = 0..10000

EXAMPLE

a(5)=3 because gpf(5)=5, gpf(4)+gpf(1)=3, gpf(3)+gpf(2)=5, gpf(3)+2*gpf(1)=5, 2*gpf(2)+gpf(1)=5, gpf(2)+3*gpf(1)=5, 5*gpf(1)=5.

MAPLE

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

       min(b(n, i-1), `if`(i>n, infinity, b(n-i, i)+

       max(map(h-> h[1], ifactors(i)[2])[]))))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..120);  # Alois P. Heinz, Apr 15 2015

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0 || i==1, n, Min[b[n, i-1], If[i>n, Infinity, b[n-i, i]+Max[FactorInteger[i][[All, 1]]]]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Feb 05 2017, after Alois P. Heinz *)

PROG

(Haskell)

a128630 n = a128630_list !! (n-1)

a128630_list = map (minimum . map (sum . map (gpfs !!))) $ tail pss where

   pss = [] : map parts [1..] :: [[[Int]]] where

         parts u = [u] : [v : ps | v <- [1..u],

                                   ps <- pss !! (u - v), v < head ps]

   gpfs = map fromInteger (0 : map a006530 [1..])

-- Reinhard Zumkeller, Apr 13 2015

CROSSREFS

Cf. A128631.

Cf. A006530.

Sequence in context: A261461 A078627 A106370 * A273040 A319982 A304331

Adjacent sequences:  A128627 A128628 A128629 * A128631 A128632 A128633

KEYWORD

nonn

AUTHOR

Logan Kleinwaks (kleinwaks(AT)alumni.princeton.edu), Mar 15 2007

STATUS

approved

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)