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A225730
Numbers k such that k < d(k)^(22/10), where d(k) is the number of divisors of k.
3
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).
Sequence in context: A225731 A246352 A363227 * A256389 A225729 A035033
KEYWORD
nonn,fini,full
AUTHOR
T. D. Noe, May 14 2013
STATUS
approved