login
Numbers k such that k < d(k)^2, where d(k) = A000005(k).
32

%I #38 May 08 2023 23:32:46

%S 2,3,4,6,8,10,12,14,15,16,18,20,24,28,30,32,36,40,42,48,54,56,60,72,

%T 80,84,90,96,108,120,126,132,140,144,168,180,192,210,216,240,252,288,

%U 300,336,360,420,480,504,540,720,840,1260

%N Numbers k such that k < d(k)^2, where d(k) = A000005(k).

%C See comment in A175495. - _Vladimir Shevelev_, May 07 2013

%C The deficient terms are 2, 3, 4, 8, 10, 14, 15, 16, 32; the first perfect or abundant number not listed is 66 = 2 * 3 * 11; the only term not 7-smooth is 132 = 2^2 * 3 * 11; the largest not divisible by 6 is 140 = 2^2 * 5 * 7. - _Peter Munn_, Sep 19 2021

%C The union of this sequence and A276734 has 74 total terms which are all k with floor(sqrt(k)) <= d(k). - _Bill McEachen_, Apr 07 2023

%t Select[Range[1300],#<DivisorSigma[0,#]^2&] (* _Harvey P. Dale_, Apr 11 2014 *)

%o (PARI) isok(n) = (n < numdiv(n)^2) \\ _Michel Marcus_, Jun 07 2013

%Y Cf. A000005, A035033, A035034, A035035, A033950, A036763, A175495, A276734.

%K nonn,fini,full

%O 1,1

%A _Erich Friedman_

%E _Labos Elemer_ added the last three terms and observes that this sequence is now complete.