A248979 Numbers n such that 11 is not a divisor of A002805(11*n).

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

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: A354916 A134037 A138841 * A246409 A211837 A138863

Adjacent sequences: A248976 A248977 A248978 * A248980 A248981 A248982

Keyword

nonn

Author

Matthijs Coster, Oct 18 2014

Status

approved