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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
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 30 21:42 EST 2023. Contains 359947 sequences. (Running on oeis4.)