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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).

%I A260798 #25 May 20 2018 11:35:24
%S A260798 0,0,1,3,13,23,65,104,252,846,1237,3659,7244,10086,19195,48341,116599,
%T A260798 155037,356168,609236,792905,1716485,2832213,5887815,15116625,
%U A260798 23911833,29983570,46873052,58443395,90374471,394641602,593224103,1082063335,1318608063,3477935702,4207389268,7398721009,12885091292,18555597522,31831360281,54145147464,64517020844
%N 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).
%H A260798 Alois P. Heinz, <a href="/A260798/b260798.txt">Table of n, a(n) for n = 1..2000</a> (first 781 terms from Reinhard Zumkeller)
%e A260798 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.
%p A260798 b:= proc(n, i) option remember; `if`(n=0 or i=2, 1-irem(n, 2),
%p A260798       `if`(i<2, 0, b(n, i-1)+b(n-i, min(i, n-i))))
%p A260798     end:
%p A260798 a:= n-> (p-> b(p, p-1))(ithprime(n)):
%p A260798 seq(a(n), n=1..45);  # _Alois P. Heinz_, Mar 11 2018
%t A260798 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]]]];
%t A260798 a[n_] := b[#, # - 1]&[Prime[n]];
%t A260798 Table[a[n], {n, 1, 45}] (* _Jean-François Alcover_, May 20 2018, after _Alois P. Heinz_ *)
%o A260798 (Haskell)
%o A260798 import Data.MemoCombinators (memo2, integral)
%o A260798 a260798 n = a260798_list !! (n-1)
%o A260798 a260798_list = map (subtract 1 . pMemo 2) a000040_list where
%o A260798    pMemo = memo2 integral integral p
%o A260798    p _ 0 = 1
%o A260798    p k m | m < k     = 0
%o A260798          | otherwise = pMemo k (m - k) + pMemo (k + 1) m
%o A260798 -- _Reinhard Zumkeller_, Aug 09 2015
%Y A260798 This is A098743(prime(n)). Cf. A260797.
%Y A260798 Cf. A000040, A058698.
%K A260798 nonn
%O A260798 1,4
%A A260798 _Marc LeBrun_ and _N. J. A. Sloane_, Aug 07 2015