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).

3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 27, 29, 31, 33, 34, 35, 36, 37, 38, 39, 41, 43, 46, 47, 51, 53, 55, 57, 58, 59, 60, 61, 62, 65, 67, 69, 71, 72, 73, 74, 77, 79, 82, 83, 84, 85, 86, 87, 89, 90, 91, 93, 94, 95, 96, 97, 100, 101, 103, 106, 107, 108, 109

Offset: 1

Author

Matthew Vandermast, Mar 16 2003

Keywords

• easy
• nonn

Examples

			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).
		

References

• 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.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A182859.

Programs

Maple

A036459:= proc(n) option remember;
  procname(numtheory:-tau(n))+1;
end proc:
A036459(1):= 0: A036459(2):= 0:
select(t -> A036459(t)::odd, [$1..1000]); # Robert Israel, Aug 31 2015

Mathematica

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 *)