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A046952
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Sets record for f(n) = |{(a,b):a*b=n and a|b}|. Also squares of highly composite numbers A002182.
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11
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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
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OFFSET
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1,2
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COMMENTS
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Invented by the HR automatic theory formation program.
Also, integers whose number of square divisors sets a new record.
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
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LINKS
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FORMULA
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EXAMPLE
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f(1)=1, (first with 1), f(4)=2 (first with 2), f(16)=3 (first with 3).
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CROSSREFS
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Cf. A350756 (similar, with triangular divisors).
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KEYWORD
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nice,nonn
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AUTHOR
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Simon Colton (simonco(AT)cs.york.ac.uk)
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STATUS
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approved
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