A071864 Nonprime n such that the number of elements in the continued fraction for Sum_{d|n} 1/d equals tau(n), the number of divisors of n.

1, 4, 9, 14, 15, 21, 25, 49, 51, 55, 57, 63, 95, 98, 99, 115, 116, 121, 147, 161, 169, 172, 175, 188, 195, 203, 236, 244, 245, 247, 265, 284, 287, 289, 297, 299, 322, 328, 329, 351, 356, 361, 363, 370, 371, 374, 387, 406, 412, 413, 418, 423, 425, 437, 465, 488

Offset

1,2

Comments

If p is prime p^2 is in the sequence since the continued fraction for Sum_{d|n} 1/d is [1, p-1, p+1] and there are 3 divisors for p^2.

Links

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

Mathematica

aQ[n_] := ! PrimeQ[n] && Length@ContinuedFraction[DivisorSigma[1, n]/n] ==  DivisorSigma[0, n]; Select[Range[488], aQ] (* Amiram Eldar, Aug 30 2019 *)

Prog

(PARI) for(n=1, 1000, if(length(contfrac(sumdiv(n, d, 1/d)))==numdiv(n)*(1-isprime(n)), print1(n, ", ")))

Crossrefs

Cf. A000005, A017665, A017666, A071862.

Sequence in context: A244037 A091880 A141560 * A312987 A050986 A284956

Adjacent sequences: A071861 A071862 A071863 * A071865 A071866 A071867

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 09 2002

Status

approved