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

1,1

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

Links

Table of n, a(n) for n=1..60.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A361797 (even terms).

Cf. A075026, A075027.

Sequence in context: A336366 A088502 A081001 * A075394 A158439 A124112

Adjacent sequences: A075022 A075023 A075024 * A075026 A075027 A075028

Keyword

nonn

Author

Amarnath Murthy, Sep 02 2002

Extensions

Corrected and extended by Jason Earls, Sep 04 2002

Status

approved