cp's OEIS Frontend

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

%I A190266 #19 Oct 20 2024 02:08:32
%S A190266 7,1241,1673,1751,1769,2471,2839,3161,3305,3497,3711,4135,4265,4279,
%T A190266 4471,4711,5191,5433,5561,6017,6041,6103,6313,6809,6953,7031,7241,
%U A190266 7463,7671,8023,8057,8345,8791,8889,9079,10167,10793,10841,11111,11209,11391,11751,12297,12729
%N A190266 Numbers k such that tau(k-1) = (tau(k))^2 = tau(k+1), where tau(k) = A000005(k) (number of divisors of k).
%H A190266 Amiram Eldar, <a href="/A190266/b190266.txt">Table of n, a(n) for n = 1..10000</a>
%F A190266 A000005(a(n)-1) = (A000005(a(n)))^2 = A000005(a(n)+1).
%e A190266 a(1)=7 because tau(6) = (tau(7))^2 = tau(8) = 4;
%e A190266 a(2)=1241 because tau(1240) = (tau(1241))^2 = tau(1242) = 16.
%t A190266 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 A190266 (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 A190266 Cf. A000005, A074757, A090502. Subsequence of A036436.
%K A190266 nonn
%O A190266 1,1
%A A190266 _Juri-Stepan Gerasimov_, May 06 2011
%E A190266 Data corrected by _Amiram Eldar_, Jul 17 2019