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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

%I

%S 7,1241,1673,1751,1769,2471,2839,3161,3305,3497,3711,4135,4265,4279,

%T 4471,4711,5191,5433,5561,6017,6041,6103,6313,6809,6953,7031,7241,

%U 7463,7671,8023,8057,8345,8791,8889,9079,10167,10793,10841,11111,11209,11391,11751,12297,12729

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

%H Amiram Eldar, <a href="/A190266/b190266.txt">Table of n, a(n) for n = 1..10000</a>

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

%e a(1)=7 because tau(6) = (tau(7))^2 = tau(8) = 4;

%e a(2)=1241 because tau(1240) = (tau(1241))^2 = tau(1242) = 16.

%t 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 *)

%o (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

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

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, May 06 2011

%E Data corrected by _Amiram Eldar_, Jul 17 2019

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Last modified April 9 10:52 EDT 2020. Contains 333348 sequences. (Running on oeis4.)