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 A352974 Numbers k > 1 such that tau(k^2-1) + 1 = tau(k^2) = tau(k^2+1) - 1, tau = A000005. 1

%I

%S 165182,1395182,3262682,3977318,5360182,5937682,6899818,7582682,

%T 9542318,11345182,11612318,12167318,12624818,16427318,18770182,

%U 21622682,22109818,24389818,24437318,26750182,33504818,34657682,49904818,53542318,55172318,55695182

%N Numbers k > 1 such that tau(k^2-1) + 1 = tau(k^2) = tau(k^2+1) - 1, tau = A000005.

%C If tau(m-1) + 1 = tau(m) = tau(m+1) - 1, then m must be a square.

%C All known terms are of the form 2*p, where p is a prime congruent to 91 or -91 modulo 1250. Is this a coincidence?

%H Jianing Song, <a href="/A352974/b352974.txt">Table of n, a(n) for n = 1..51</a>

%e 165182 is a term since tau(165182^2-1) = 8, tau(165182^2) = 9, tau(165182^2+1) = 10.

%o (PARI) isA352974(n) = (n>1) && (numdiv(n^2-1) == numdiv(n^2)-1) && (numdiv(n^2+1) == numdiv(n^2)+1)

%Y Cf. A000005.

%K nonn,hard

%O 1,1

%A _Jianing Song_, Apr 13 2022

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Last modified March 31 03:22 EDT 2023. Contains 361626 sequences. (Running on oeis4.)