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A046952 Sets record for f(n) = |{(a,b):a*b=n and a|b}|. Also squares of highly composite numbers A002182. 11
1, 4, 16, 36, 144, 576, 1296, 2304, 3600, 14400, 32400, 57600, 129600, 518400, 705600, 1587600, 2822400, 6350400, 25401600, 57153600, 101606400, 228614400, 406425600, 635040000, 768398400, 2057529600, 2540160000, 3073593600 (list; graph; refs; listen; history; text; internal format)
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
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
Cf. A350756 (similar, with triangular divisors).
Sequence in context: A277285 A136404 A176471 * A318278 A293708 A081456
KEYWORD
nice,nonn
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)