A075025 Numbers k such that d(k) < d(k-1) and d(k) < d(k+1), where d(k) is the number of divisors of k.

5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 111, 113, 115, 121, 125, 127, 129, 131, 137, 139, 149, 151, 153, 155, 157, 161, 163, 167, 169, 173, 175, 179, 181, 183

Offset: 1

Author

Amarnath Murthy, Sep 02 2002

Keywords

• nonn

Comments

All primes > 3 are members.

Is this sequence of positive density? I expect a(n) ~ 4n but can only prove n (log log n)^k/ log n << a(n) << n for arbitrary k. - Charles R Greathouse IV, May 01 2011

Number of terms < 10^k: 3, 32, 324, 3222, 32026, 318583, 3181133, 31766404, ..., . - Robert G. Wilson v, May 01 2011

Examples

			17 is in the sequence because d(16) = 5, d(17) = 2, d(18) = 6 and 5 > 2 < 6.
		

Crossrefs

Cf. A000005, A361797 (even terms).

Cf. A075026, A075027.

Programs

Mathematica

fQ[n_] := DivisorSigma[0, n - 1] > DivisorSigma[0, n] < DivisorSigma[0, n + 1]; Select[ Range@ 200, fQ] (* Robert G. Wilson v, May 01 2011 *)

PARI

isok(k) = if (k>1, numdiv(k) < min(numdiv(k-1), numdiv(k+1))); \\ Michel Marcus, Mar 26 2023

Extensions

Corrected and extended by Jason Earls, Sep 04 2002