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

165182, 1395182, 3262682, 3977318, 5360182, 5937682, 6899818, 7582682, 9542318, 11345182, 11612318, 12167318, 12624818, 16427318, 18770182, 21622682, 22109818, 24389818, 24437318, 26750182, 33504818, 34657682, 49904818, 53542318, 55172318, 55695182

Offset

1,1

Comments

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

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?

Links

Jianing Song, Table of n, a(n) for n = 1..51

Example

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

Prog

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

Crossrefs

Cf. A000005.

Sequence in context: A233706 A233701 A224582 * A327942 A201051 A233425

Adjacent sequences: A352971 A352972 A352973 * A352975 A352976 A352977

Keyword

nonn,hard

Author

Jianing Song, Apr 13 2022

Status

approved