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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).
7
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
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
KEYWORD
easy,nonn
AUTHOR
Matthew Vandermast, Mar 16 2003
STATUS
approved