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 A081401 #21 Jun 28 2020 16:13:58
%S A081401 0,1,3,5,8,11,15,18,22,26,31,35,41,46,51,55,62,67,75,80,86,92,101,106,
%T A081401 112,119,125,131,141,147,158,163,170,178,185,191,203,212,220,226,239,
%U A081401 246,260,267,274,284,299,305,313,320,329,337,353,360,368,375,385,396,413
%N A081401 Pseudologarithm (A056239) of n!: a(n) = A056239(A000142(n)).
%C A081401 As A056239 is fully additive sequence, this sequence gives its partial sums. - _Antti Karttunen_, Jun 28 2020
%H A081401 Alois P. Heinz, <a href="/A081401/b081401.txt">Table of n, a(n) for n = 1..1000</a>
%F A081401 a(n) = Sum(k*e(k)) where k runs through indices of prime factors of n!, while e(k) is the exponent of the corresponding prime factor.
%e A081401 n=8: 8! = 40320 = 2*2*2*2*2*2*2*3*3*5*7, p-indices = {1,2,3,4}, exponents = {7,2,1,1}; a(8) = 1*7 + 2*2 + 3*1 + 4*1 = 7 + 4 + 3 + 4 = 18.
%p A081401 a:= n-> add (numtheory[pi](i[1])*i[2], i=ifactors(n!)[2]):
%p A081401 seq (a(n), n=1..100); # _Alois P. Heinz_, Aug 09 2012
%t A081401 Array[Total[FactorInteger[#!] /. {p_, c_} /; p > 0 :> PrimePi[p] c] &, 59] (* _Michael De Vlieger_, Jun 26 2020 *)
%Y A081401 Cf. A000142, A056239.
%Y A081401 Cf. also A335860.
%K A081401 nonn
%O A081401 1,3
%A A081401 _Labos Elemer_, Mar 31 2003