OFFSET
1,2
COMMENTS
Invented by the HR automatic theory formation program.
From Bernard Schott, Jan 14 2022: (Start)
Also, integers whose number of square divisors sets a new record.
As a(n) is the square of n-th highly composite number (A002182), the record number of square divisors of a(n) is A046951(a(n)) = tau(A002182(n)) = A002183(n) where tau is the divisor counting function (A000005). - Bernard Schott, Jan 15 2022
Integers m for which number of solutions (A353282) to the Diophantine equation S(x,y) = (x+y) + (x-y) + (x*y) + (x/y) = m sets a new record; these records are respectively 0, 1, 2, 3, 5, 7, ... Example: the 5 solutions for S(x,y) = 144 are (36,1), (32,2), (27,3), (20,5), (11,11). - Bernard Schott, Apr 19 2022
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
FORMULA
a(n) = A002182(n)^2. - Bernard Schott, Jan 14 2022
EXAMPLE
f(1)=1, (first with 1), f(4)=2 (first with 2), f(16)=3 (first with 3).
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
STATUS
approved