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%I #11 Feb 14 2024 01:04:55
%S 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 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 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 Sum of A034968(d) over divisors d of n, where A034968 gives the sum of digits in factorial base.
%C Inverse Möbius transform of A034968.
%H Antti Karttunen, <a href="/A319712/b319712.txt">Table of n, a(n) for n = 1..40320</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%F a(n) = Sum_{d|n} A034968(d).
%F a(n) = A319711(n) + A034968(n).
%t 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 (PARI)
%o A034968(n) = { my(s=0, b=2, d); while(n, d = (n%b); s += d; n = (n-d)/b; b++); (s); };
%o A319712(n) = sumdiv(n,d,A034968(d));
%Y Cf. A034968, A319711, A319715.
%K nonn,base
%O 1,2
%A _Antti Karttunen_, Oct 02 2018
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