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A190266 Numbers k such that tau(k-1) = (tau(k))^2 = tau(k+1), where tau(k) = A000005(k)(number of divisors of k). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)