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%I #17 Feb 07 2024 01:17:03
%S 0,1,2,1,2,3,3,2,2,4,3,2,2,3,4,1,3,5,4,4,3,5,3,3,3,4,5,2,4,4,5,3,2,5,
%T 4,3,3,4,4,3,3,5,6,5,4,5,3,3,3,4,5,3,5,6,5,3,4,6,5,4,4,5,6,3,5,6,4,4,
%U 4,5,5,4,4,5,5,4,4,4,6,5,2,6,5,3,4,4,5
%N a(n) = A060130(A000217(n)); number of nonzero digits in factorial base representation (A007623) of 0+1+2+...+n.
%C The next 1 after a(1), a(3) and a(15) occurs at n=224, as A000217(224) = 25200 = 5 * 7!.
%H Antti Karttunen, <a href="/A232094/b232094.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = A060130(A000217(n)).
%F a(n) = A230410(A226061(n+1)). [Not a practical way to compute this sequence. Please see comments at A230410.]
%t a[n_] := Module[{k = n*(n+1)/2, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; Count[s, _?(# > 0 &)]]; Array[a, 100, 0] (* _Amiram Eldar_, Feb 07 2024 *)
%o (Scheme)
%o (define (A232094 n) (A060130 (A000217 n)))
%Y Cf. A000217, A007623, A060130, A226061, A230410, A232095.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, Nov 18 2013
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