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

Author

Matthijs Coster, Oct 18 2014

Keywords

• nonn

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?

Examples

			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.
		

Crossrefs

Cf. A002805.

Programs

PARI

lista(nn) = {forstep (n=0, nn, 11, if (denominator(sum(k=2,n,1/k)) % 11, print1(n, ", ")););} \\ Michel Marcus, Oct 19 2014

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