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 A319712 #11 Feb 14 2024 01:04:55
%S A319712 1,2,3,4,4,5,3,6,6,8,5,9,4,7,10,10,6,11,5,14,10,11,7,12,6,7,9,12,5,17,
%T A319712 4,13,11,11,11,18,5,10,11,21,7,19,6,18,19,14,8,18,6,13,12,13,6,17,12,
%U A319712 18,12,11,7,29,6,10,19,19,14,23,7,19,16,25,9,24,5,10,17,17,13,19,6,30,15,14,8,31,15,13,14,27,9,35,13,23,14,17,17
%N A319712 Sum of A034968(d) over divisors d of n, where A034968 gives the sum of digits in factorial base.
%C A319712 Inverse Möbius transform of A034968.
%H A319712 Antti Karttunen, <a href="/A319712/b319712.txt">Table of n, a(n) for n = 1..40320</a>
%H A319712 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%F A319712 a(n) = Sum_{d|n} A034968(d).
%F A319712 a(n) = A319711(n) + A034968(n).
%t A319712 d[n_] := Module[{k = n, m = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, s += r; m++]; s]; a[n_] := DivisorSum[n, d[#] &]; Array[a, 100] (* _Amiram Eldar_, Feb 14 2024 *)
%o A319712 (PARI)
%o A319712 A034968(n) = { my(s=0, b=2, d); while(n, d = (n%b); s += d; n = (n-d)/b; b++); (s); };
%o A319712 A319712(n) = sumdiv(n,d,A034968(d));
%Y A319712 Cf. A034968, A319711, A319715.
%K A319712 nonn,base
%O A319712 1,2
%A A319712 _Antti Karttunen_, Oct 02 2018