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%I #38 Mar 19 2020 11:14:47
%S 0,33,77,110,847,880,924,957,1210,1243,1287,1320,9328,9372,9416,9702,
%T 9768,10538,10582,10626,14201,14223,102608,102641,102685,102718,
%U 103136,103158,116413,116457,116501,156255,156277,1128688,1128721,1128765,1128798,1129073
%N Numbers n such that 11 is not a divisor of A002805(11*n).
%C For other primes after a few exceptions it seems that all denominators of harmonic numbers are divisible by that prime. For 11 there are many more exceptions. Maybe infinitely many?
%e 33 is in the sequence since H(33) = p/q and 11 is not a divisor of q. Here H(n) = Sum_{i=1..n} 1/i.
%e Of course if H(33) has no denominator with a factor 11 the same is true for 34, 35, ..., 43.
%o (Sage)
%o n = 10000
%o sum11 = 0
%o resu = [0]
%o for i in range(11, n, 11):
%o D = (1 / i).partial_fraction_decomposition()[1]
%o sum11 += sum(v for v in D if 11.divides(v.denominator()))
%o if sum11 >= 1:
%o sum11 -= 1
%o if sum11 == 0:
%o resu.append(i)
%o resu
%o (PARI) lista(nn) = {forstep (n=0, nn, 11, if (denominator(sum(k=2,n,1/k)) % 11, print1(n, ", ")););} \\ _Michel Marcus_, Oct 19 2014
%Y Cf. A002805.
%K nonn
%O 1,2
%A _Matthijs Coster_, Oct 18 2014
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