This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384936 #9 Jun 18 2025 23:46:58
%S A384936 0,1,3,9,16,28,42,57,76,97,121,148,177,208,242,279,316,359,401,446,
%T A384936 493,545,596,651,708,767,829,893,958,1026,1096,1170,1246,1319,1400,
%U A384936 1484,1567,1657,1742,1834,1923,2021,2119,2218,2316,2419,2526,2635,2745,2857,2972
%N A384936 a(n) = Sum_{k=1..n} floor( log(A002110(n)) / log(prime(k)) ).
%C A384936 A384442(a(n)) = A002110(n) for n <= 8; does it hold for n > 5?
%H A384936 Michael De Vlieger, <a href="/A384936/b384936.txt">Table of n, a(n) for n = 0..10000</a>
%F A384936 a(n) = A361373(A002110(n)).
%F A384936 Row sums of A287010.
%e A384936 Table of n, a(n) for n = 0..10, listing terms in row n of A287010:
%e A384936 Terms in row n of A287010 corresponding
%e A384936 to the primes listed in the header
%e A384936 n\k 2 3 5 7 11 13 17 19 23 29 a(n)
%e A384936 ---------------------------------------------------
%e A384936 0: 0 . . . . . . . . . 0
%e A384936 1: 1 . . . . . . . . . 1
%e A384936 2: 2 1 . . . . . . . . 3
%e A384936 3: 4 3 2 . . . . . . . 9
%e A384936 4: 7 4 3 2 . . . . . . 16
%e A384936 5: 11 7 4 3 3 . . . . . 28
%e A384936 6: 14 9 6 5 4 4 . . . . 42
%e A384936 7: 18 11 8 6 5 5 4 . . . 57
%e A384936 8: 23 14 9 8 6 6 5 5 . . 76
%e A384936 9: 27 17 11 9 8 7 6 6 6 . 97
%e A384936 10: 32 20 14 11 9 8 7 7 7 6 121
%t A384936 P = 2; s = {2}; {0}~Join~Reap[Do[Sow@ Total@ Map[Floor@ Log[#, P] &, s]; (AppendTo[s, #]; P *= #) &[Prime[k]], {k, 2, 51}] ][[-1, 1]]
%o A384936 (PARI) a(n) = my(v=primes(n), pp=vecprod(v)); sum(k=1, n, log(pp)\log(v[k])); \\ _Michel Marcus_, Jun 14 2025
%Y A384936 Cf. A002110, A287010, A361373, A377485, A384442.
%K A384936 nonn,easy
%O A384936 0,3
%A A384936 _Michael De Vlieger_, Jun 12 2025