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A323701 a(n) is the number of primes p such that A007504(n) <= p < A007504(n+1).

%I A323701 #16 Jun 29 2025 11:07:19
%S A323701 2,2,2,3,3,4,5,4,6,6,7,7,8,7,9,10,10,8,12,12,11,12,12,15,14,14,14,14,
%T A323701 17,17,16,17,19,19,22,16,24,21,20,20,20,28,22,26,21,24,28,23,31,23,30,
%U A323701 28,28,32,28,31,30,27,35,30,32,31,38,34,38,36,36,37,35,35
%N A323701 a(n) is the number of primes p such that A007504(n) <= p < A007504(n+1).
%C A323701 Corresponds to the number of terms in A321578 which are equal to n.
%H A323701 Michael De Vlieger, <a href="/A323701/b323701.txt">Table of n, a(n) for n = 1..10000</a>
%e A323701 a(1)=2 because 2 <= 2, 3 < 5;
%e A323701 a(5)=3 because 28 <= 29, 31, 37 < 41.
%t A323701 nn = 1375; MapIndexed[Set[s[First[#2]], #1] &, Accumulate[Prime@ Range[nn]]]; c = 0; j = k = 1; Rest@ Reap[Do[p = Prime[n]; While[s[k] <= p, k++]; If[j == k, c++, Sow[c + 1]; c = 0]; j = k, {n, nn}] ][[-1, 1]] (* _Michael De Vlieger_, Jun 29 2025 *)
%o A323701 (Perl) use ntheory ':all'; sub a { my $p = nth_prime($_[0]+1); my $s = sum_primes($p); prime_count($s-$p, $s-1) }; print join(", ", map { a($_) } 1..100), "\n"; # _Daniel Suteu_, Jan 25 2019
%Y A323701 Cf. A000040, A007504, A321578, A061568.
%K A323701 nonn
%O A323701 1,1
%A A323701 _David James Sycamore_, Jan 24 2019
%E A323701 More terms from _Daniel Suteu_, Jan 25 2019