[seqfan] Re: checking A179385 (parts equal to 1 in restricted partitions of n)

[Alois Heinz]

I do confirm your evaluation:

b:= proc(n,i) option remember;
   if n<=0 then 0
 elif i=0 then n
 else b(n, i-1) +b(n-ithprime(i), i-1)
   fi
end:
a:= n-> b (n, numtheory[pi](n)):
seq (a(n), n=1..80);

 1, 2, 4, 7, 10, 15, 20, 27, 35, 44, 55, 67, 81, 97, 115, 135, 158, 183, 
212,
 244, 280, 320, 364, 413, 467, 526, 591, 661, 737, 820, 909, 1007, 1112, 
1226,
 1349, 1481, 1624, 1778, 1943, 2121, 2311, 2515, 2734, 2968, 3219, 3486, 
3771,
 4075, 4399, 4744, 5112, 5502, 5917, 6358, 6826, 7324, 7851, 8410, 9001, 
9627,
 10290, 10992, 11734, 12518, 13346, 14219, 15142, 16115, 17141, 18222, 
19360,
 20559, 21822, 23152, 24552, 26023, 27570, 29195, 30903, 32698

Alois

Richard Mathar schrieb:
> I am unable to reproduce http://oeis.org/classic/A179385
> (count of parts equal to 1 in all partitions of n, all parts
> either 1 or prime, and no repeated prime in any partition)
> but get instead
> 1, 2, 4, 7, 10, 15, 20, 27, 35, 44, 55, 67, 81, 97, 115, 135, 158, 183, 212,
>     244, 280, 320, 364, 413, 467, 526, 591, 661, 737, 820, 909, 1007, 1112,
>     1226, 1349
>
> Can someone confirm/check this modification?
>