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

1,1

Comments

Numbers m such that m^2-1 is divisible by d(m^2-1), m^2 is divisible by d(m^2) and d(m^2) > d(m^2-1), d = A000005.

The smallest term not divisible by 3 is a(1048) = 2907025.

Links

Jianing Song, Table of n, a(n) for n = 1..1500

Example

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.

Prog

(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)

Crossrefs

Cf. A000005, A033950, A342969.

Sequence in context: A249537 A156845 A174851 * A284970 A183007 A251087

Adjacent sequences: A342967 A342968 A342969 * A342971 A342972 A342973

Keyword

nonn

Author

Jianing Song, Apr 01 2021

Status

approved