A190266 Numbers k such that tau(k-1) = (tau(k))^2 = tau(k+1), where tau(k) = A000005(k) (number of divisors of k).

7, 1241, 1673, 1751, 1769, 2471, 2839, 3161, 3305, 3497, 3711, 4135, 4265, 4279, 4471, 4711, 5191, 5433, 5561, 6017, 6041, 6103, 6313, 6809, 6953, 7031, 7241, 7463, 7671, 8023, 8057, 8345, 8791, 8889, 9079, 10167, 10793, 10841, 11111, 11209, 11391, 11751, 12297, 12729

Offset

1,1

Links

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

Formula

A000005(a(n)-1) = (A000005(a(n)))^2 = A000005(a(n)+1).

Example

a(1)=7 because tau(6) = (tau(7))^2 = tau(8) = 4;
a(2)=1241 because tau(1240) = (tau(1241))^2 = tau(1242) = 16.

Mathematica

Transpose[Select[Partition[Range[15000], 3, 1], DivisorSigma[0, #[[2]]]^2 == DivisorSigma[0, First[#]] == DivisorSigma[0, Last[#]]&]][[1]] + 1 (* Amiram Eldar, Jul 17 2019 after Harvey P. Dale at A175116 *)

Prog

(PARI) isA190266(n)=my(t=numdiv(n-1)); issquare(t) & t==numdiv(n+1) & t==numdiv(n)^2 \\ Charles R Greathouse IV, May 14 2011

Crossrefs

Cf. A000005, A074757, A090502. Subsequence of A036436.

Sequence in context: A229431 A159994 A278178 * A119181 A152518 A210396

Adjacent sequences: A190263 A190264 A190265 * A190267 A190268 A190269

Keyword

nonn

Author

Juri-Stepan Gerasimov, May 06 2011

Extensions

Data corrected by Amiram Eldar, Jul 17 2019

Status

approved