cp's OEIS Frontend

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.

%I A075025 #28 Mar 28 2023 02:43:04
%S A075025 5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,51,53,55,59,61,65,67,69,
%T A075025 71,73,77,79,83,89,91,97,101,103,107,109,111,113,115,121,125,127,129,
%U A075025 131,137,139,149,151,153,155,157,161,163,167,169,173,175,179,181,183
%N 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.
%C A075025 All primes > 3 are members.
%C A075025 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
%C A075025 Number of terms < 10^k: 3, 32, 324, 3222, 32026, 318583, 3181133, 31766404, ..., . - _Robert G. Wilson v_, May 01 2011
%e A075025 17 is in the sequence because d(16) = 5, d(17) = 2, d(18) = 6 and 5 > 2 < 6.
%t A075025 fQ[n_] := DivisorSigma[0, n - 1] > DivisorSigma[0, n] < DivisorSigma[0, n + 1]; Select[ Range@ 200, fQ] (* _Robert G. Wilson v_, May 01 2011 *)
%o A075025 (PARI) isok(k) = if (k>1, numdiv(k) < min(numdiv(k-1), numdiv(k+1))); \\ _Michel Marcus_, Mar 26 2023
%Y A075025 Cf. A000005, A361797 (even terms).
%Y A075025 Cf. A075026, A075027.
%K A075025 nonn
%O A075025 1,1
%A A075025 _Amarnath Murthy_, Sep 02 2002
%E A075025 Corrected and extended by _Jason Earls_, Sep 04 2002