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A036764
If n can be expressed as m/d(m) for some m, where d(m) is the number of divisors of m (A000005), then a(n) is the smallest such m, otherwise a(n) = 0.
4
1, 8, 9, 36, 40, 72, 56, 80, 108, 180, 88, 240, 104, 252, 360, 128, 136, 0, 152, 480, 504, 396, 184, 384, 225, 468, 0, 560, 232, 0, 248, 448, 792, 612, 1260, 864, 296, 684, 936, 640, 328, 1680, 344, 880, 0, 828, 376, 1152, 441, 1800, 1224, 1040, 424, 972, 1980
OFFSET
1,2
COMMENTS
If a(n) = q (say) is not zero, then x = q*d(x) has only a finite number of solutions. See A036763 for the numbers which cannot be expressible as m/d(m) for some m.
a(9p) = 0 for all primes p. - Jianing Song, Nov 25 2018
LINKS
EXAMPLE
If q=25 then 25*9 = 225, 25*18 = 450 and 25*24 = 600 so that d(225), d(450), d(600) are 9, 18, 24, respectively. The smallest is 225. Thus a(25)=225.
MAPLE
with(numtheory): A036764 := proc(n) local k, p: for k from 1 to 4*n^2 do p:=n*k: if(p=n*tau(p))then return p: fi: od: return 0: end: seq(A036764(n), n=1..40); # Nathaniel Johnston, May 04 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Additional comments from Asher Auel, May 17 2001
STATUS
approved