cp's OEIS Frontend

A080218 Monotonically increasing sequence such that every positive integer n appears if and only if d(n) doesn't (d(n)=number of divisors of n, A000005).

%I A080218 #14 May 08 2018 15:11:55
%S A080218 3,5,6,7,8,10,11,13,14,15,17,19,21,22,23,26,27,29,31,33,34,35,36,37,
%T A080218 38,39,41,43,46,47,51,53,55,57,58,59,60,61,62,65,67,69,71,72,73,74,77,
%U A080218 79,82,83,84,85,86,87,89,90,91,93,94,95,96,97,100,101,103,106,107,108,109
%N A080218 Monotonically increasing sequence such that every positive integer n appears if and only if d(n) doesn't (d(n)=number of divisors of n, A000005).
%D A080218 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
%H A080218 Robert Israel, <a href="/A080218/b080218.txt">Table of n, a(n) for n = 1..10000</a>
%H A080218 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%e A080218 d(1)=1 and d(2)=2; therefore neither are included. Members include 3 (2 divisors), 6 (4 divisors) and 60 (12 divisors); other nonmembers include 4 (3 divisors), 12 (6 divisors) and 5040 (60 divisors).
%p A080218 A036459:= proc(n) option remember;
%p A080218   procname(numtheory:-tau(n))+1;
%p A080218 end proc:
%p A080218 A036459(1):= 0: A036459(2):= 0:
%p A080218 select(t -> A036459(t)::odd, [$1..1000]); # _Robert Israel_, Aug 31 2015
%t A080218 a = {}; Do[Which[DivisorSigma[0, k] == k, 0, MemberQ[a, DivisorSigma[0, k]], 0, True, AppendTo[a, k]], {k, 109}]; a (* _Michael De Vlieger_, Aug 31 2015 *)
%Y A080218 Cf. A182859.
%K A080218 easy,nonn
%O A080218 1,1
%A A080218 _Matthew Vandermast_, Mar 16 2003