A225730 Numbers k such that k < d(k)^(22/10), where d(k) is the number of divisors of k.

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 108, 112, 120, 126, 132, 140, 144, 150, 156, 160, 168, 180, 192, 198, 200, 204, 210, 216, 220, 224, 228, 234

Offset

1,1

Comments

Alternatively, we could write k^5 < d(k)^11. The last odd number is a(23) = 45.

Links

T. D. Noe, Table of n, a(n) for n = 1..155 (complete sequence)

Mathematica

t = {}; Do[If[n < DivisorSigma[0, n]^(22/10), AppendTo[t, n]], {n, 10^5}]; t
Select[Range[250], #<DivisorSigma[0, #]^(22/10)&] (* Harvey P. Dale, Apr 10 2024 *)

Prog

(PARI) for (k=2, 20000, if (k^5 < numdiv(k)^11, print1(k, ", "))) \\ Hugo Pfoertner, Apr 25 2023

Crossrefs

Cf. A000005, A034884 (k < d(k)^2), A175495 (k < 2^d(k)), A056757 (k < d(k)^3).

Cf. A225729-A225738, A353448.

Sequence in context: A225731 A246352 A363227 * A256389 A225729 A035033

Adjacent sequences: A225727 A225728 A225729 * A225731 A225732 A225733

Keyword

nonn,fini,full

Author

T. D. Noe, May 14 2013

Status

approved