A308749 - OEIS

%I #20 Dec 08 2023 07:12:15

%S 2,1,43,7,1,1145,4,20,71,1,7,1879,376,2,458,10,1,1763,46,5,147,20,38,

%T 983,4,188,43,1,2,229,94,5,397,7,2531,988,40,23,912,4,1,6692,3,10,

%U 3769,19,62,741,63,2,1716,94,20,1783,8,589,191,1,27,430,986,47,49

%N Smallest positive m such that n*m is a partial sum of primes.

%H Alois P. Heinz, <a href="/A308749/b308749.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = A007504(A053050(n))/n.

%F a(n) = 1 <=> n in { A007504 } \ { 0 }.

%p s:= proc(n) option remember; `if`(n=0, 0, ithprime(n)+s(n-1)) end:

%p a:= proc(n) option remember; local k; for k

%p       while irem(s(k), n)>0 do od; s(k)/n

%p     end:

%p seq(a(n), n=1..70);

%t s[n_] := s[n] = If[n == 0, 0, Prime[n] + s[n-1]];

%t a[n_] := a[n] = Module[{k}, For[k = 1, True, k++, If[Mod[s[k], n] <= 0, Return[s[k]/n]]]];

%t Table[a[n], {n, 1, 70}] (* _Jean-François Alcover_, Dec 08 2023, after _Alois P. Heinz_ *)

%Y Cf. A000040, A007504, A053050.

%K nonn

%O 1,1

%A _Alois P. Heinz_, Jun 21 2019