A353448 -id:A353448 - cp's OEIS frontend

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

T. D. Noe, May 14 2013

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

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

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

Cf. A225729-A225738, A353448.

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

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

A160007 Deficient numbers more than 1 unit away from their predecessors.

Original entry on oeis.org

7, 13, 19, 21, 25, 29, 31, 37, 41, 43, 49, 55, 57, 61, 67, 71, 73, 79, 81, 85, 89, 91, 97, 101, 103, 105, 109, 113, 115, 121, 127, 133, 139, 141, 145, 151, 157, 161, 163, 169, 175, 177, 181, 187, 193, 197, 199, 201, 205, 209, 211, 217, 221, 223, 225, 229, 235

Offset: 1

Don Love (moptop35(AT)hotmail.com), Apr 29 2009

nonn

			The first dozen deficient numbers are 1,2,3,4,5,7,8,9,10,11,13,14. There are "jumps" between a(5) and a(6), and between a(10) and a(11), i.e., at 7 and 13.

Rainer Rosenthal, Table of n, a(n) for n = 1..2488

Cf. A005100 (deficient numbers).

Cf. A353448.

lista(nn) = {last = 0; for (i = 1, nn, if (sigma(i) < 2*i, if (i > last + 1, print1(i, ", ");); last = i;););} \\ Michel Marcus, Sep 02 2013

More terms from Don Love (moptop35(AT)hotmail.com), May 01 2009

cp's OEIS Frontend

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

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