

A248979


Numbers n such that 11 is not a divisor of A002805(11*n).


0



0, 33, 77, 110, 847, 880, 924, 957, 1210, 1243, 1287, 1320, 9328, 9372, 9416, 9702, 9768, 10538, 10582, 10626, 14201, 14223, 102608, 102641, 102685, 102718, 103136, 103158, 116413, 116457, 116501, 156255, 156277, 1128688, 1128721, 1128765, 1128798, 1129073
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OFFSET

1,2


COMMENTS

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?


LINKS

Table of n, a(n) for n=1..38.


EXAMPLE

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.
Of course if H(33) has no denominator with a factor 11 the same is true for 34, 35, ..., 43.


PROG

(Sage)
n = 10000
sum11 = 0
resu = [0]
for i in range(11, n, 11):
D = (1 / i).partial_fraction_decomposition()[1]
sum11 += sum(v for v in D if 11.divides(v.denominator()))
if sum11 >= 1:
sum11 = 1
if sum11 == 0:
resu.append(i)
resu
(PARI) lista(nn) = {forstep (n=0, nn, 11, if (denominator(sum(k=2, n, 1/k)) % 11, print1(n, ", ")); ); } \\ Michel Marcus, Oct 19 2014


CROSSREFS

Cf. A002805.
Sequence in context: A137187 A134037 A138841 * A246409 A211837 A138863
Adjacent sequences: A248976 A248977 A248978 * A248980 A248981 A248982


KEYWORD

nonn


AUTHOR

Matthijs Coster, Oct 18 2014


STATUS

approved



