A342970 Numbers m such that both m^2-1 and m^2 are refactorable numbers (A033950) and that m^2 has more divisors than m^2-1.
3591, 4545, 5481, 6975, 8415, 9639, 11319, 11583, 11745, 12225, 12735, 16065, 18711, 24255, 24759, 30015, 31671, 39105, 40257, 41535, 41769, 44631, 44865, 52065, 52569, 53055, 54975, 56511, 60255, 60705, 64071, 64575, 69825, 72009, 73665, 76095, 81081, 81855, 87129
Offset: 1
Keywords
Examples
5481 is a term since 5481^2-1 is divisible by d(5481^2-1) = 40, 5481^2 is divisible by d(5481^2) = 63, and 63 > 40. 2907025 is a term since 2907025^2-1 is divisible by d(2907025^2-1) = 96, 2907025^2 is divisible by d(2907025^2) = 125, and 125 > 96.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1500 from Jianing Song)
Programs
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Mathematica
q[n_] := Module[{d = DivisorSigma[0, n^2 - {1, 0}]}, d[[1]] < d[[2]] && Divisible[n^2-1, d[[1]]] && Divisible[n^2, d[[2]]]]; Select[Range[10^5], q] (* Amiram Eldar, Feb 03 2025 *) -
PARI
isA342970(n) = if(n>1, my(d1 = numdiv(n^2-1), d2 = numdiv(n^2)); !((n^2-1) % d1) && !(n^2 % d2) && d2 > d1, 0)
Comments