A260798 Number of partitions of p=prime(n) into aliquant parts (i.e., parts that do not divide p, meaning any part except 1 and p).

0, 0, 1, 3, 13, 23, 65, 104, 252, 846, 1237, 3659, 7244, 10086, 19195, 48341, 116599, 155037, 356168, 609236, 792905, 1716485, 2832213, 5887815, 15116625, 23911833, 29983570, 46873052, 58443395, 90374471, 394641602, 593224103, 1082063335, 1318608063, 3477935702, 4207389268, 7398721009, 12885091292, 18555597522, 31831360281, 54145147464, 64517020844

Offset: 1

Author

Marc LeBrun and N. J. A. Sloane, Aug 07 2015

Keywords

• nonn

Examples

			For n=4, the fourth prime is 7, and we see the three partitions 7=2+5=2+2+3=3+4, so a(4)=3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2000 (first 781 terms from Reinhard Zumkeller)

Crossrefs

This is A098743(prime(n)). Cf. A260797.

Cf. A000040, A058698.

Programs

Haskell

import Data.MemoCombinators (memo2, integral)
a260798 n = a260798_list !! (n-1)
a260798_list = map (subtract 1 . pMemo 2) a000040_list where
   pMemo = memo2 integral integral p
   p _ 0 = 1
   p k m | m < k     = 0
         | otherwise = pMemo k (m - k) + pMemo (k + 1) m
-- Reinhard Zumkeller, Aug 09 2015

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=2, 1-irem(n, 2),
      `if`(i<2, 0, b(n, i-1)+b(n-i, min(i, n-i))))
    end:
a:= n-> (p-> b(p, p-1))(ithprime(n)):
seq(a(n), n=1..45);  # Alois P. Heinz, Mar 11 2018

Mathematica

b[n_, i_] := b[n, i] = If[n == 0 || i == 2, 1 - Mod[n, 2], If[i < 2, 0, b[n, i - 1] + b[n - i, Min[i, n - i]]]];
a[n_] := b[#, # - 1]&[Prime[n]];
Table[a[n], {n, 1, 45}] (* Jean-François Alcover, May 20 2018, after Alois P. Heinz *)