A036436 Numbers whose number of divisors is a square.

1, 6, 8, 10, 14, 15, 21, 22, 26, 27, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 120, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 168, 177, 178, 183

Offset

1,2

Comments

Invented by the HR (named after Hardy and Ramanujan) concept formation program.

Numbers in this sequence but not in A036455 are 1, 1260, 1440, 1800, 1980 etc. [From R. J. Mathar, Oct 20 2008]

tau(p^(n^2-1)) = n^2 so numbers of this form are in this sequence, and because tau is multiplicative: if a and b are in this sequence and (a,b)=1 then a*b is also in a(n). - Enrique Pérez Herrero, Jan 22 2013

References

S. Colton, Automated Theorem Discovery: A Future Direction for Theorem Provers, 2002.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.

S. Colton, HR - Automatic Theory Formation in Pure Mathematics (Unfortunately [403 Forbidden])

S. Colton and A. Bundy, Automatic Concept Formation in Pure Mathematics

S. Colton, A. Bundy and T. Walsh, Agent Based Cooperative Theory Formation in Pure Mathematics

S. Colton, R. McCasland and A. Bundy, Automated Theory Formation for Tutoring Tasks in Pure Mathematics, 2002.

Example

tau(6)=4, which is a square number, so 6 is in this sequence.

Mathematica

Select[Range[200], IntegerQ[Sqrt[DivisorSigma[0, #]]]&]  (* Harvey P. Dale, Apr 20 2011 *)

Prog

(PARI) is(n)=issquare(numdiv(n)) \\ Charles R Greathouse IV, Jan 22 2013

Crossrefs

Cf. A009087, A033950, A057265, A049439.

Sequence in context: A328338 A365535 A120497 * A036455 A291127 A211337

Adjacent sequences: A036433 A036434 A036435 * A036437 A036438 A036439

Keyword

easy,nonn

Author

Simon Colton (simonco(AT)cs.york.ac.uk)

Extensions

Links corrected and edited by Daniel Forgues, Jun 30 2010

Status

approved