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

1,1

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].

Example

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).

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 *)

Crossrefs

Cf. A182859.

Sequence in context: A181744 A343217 A160685 * A080651 A047330 A093511

Adjacent sequences: A080215 A080216 A080217 * A080219 A080220 A080221

Keyword

easy,nonn

Author

Matthew Vandermast, Mar 16 2003

Status

approved