This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056793 #62 Aug 20 2023 17:01:43
%S A056793 1,2,4,6,12,12,24,32,48,48,96,96,192,192,192,240,480,480,960,960,960,
%T A056793 960,1920,1920,2880,2880,3840,3840,7680,7680,15360,18432,18432,18432,
%U A056793 18432,18432,36864,36864,36864,36864,73728,73728,147456,147456,147456,147456
%N A056793 Number of divisors of lcm(1..n).
%C A056793 The ratio a(n)/a(n-1) equals 1 if n is a member of A024619, equals 2 if n is prime, and is a noninteger value if n is in A025475. The noninteger ratio never seems to exceed 3/2, but appears to equal 3/2 if n is a member of A001248. The noninteger ratio conforms to the formula 1/(1 - 1/n), which has 1 for limit and only 2 as single integer solution. In terms of coordinates (x,y), the lower values are (1/(1-1/n), 2^(n-1)) for n > 2. - _Eric Desbiaux_, Jul 28 2013
%C A056793 Conjectured partial sums of A101207. - _Sean A. Irvine_, Jun 25 2022
%H A056793 Nathaniel Johnston, <a href="/A056793/b056793.txt">Table of n, a(n) for n = 1..1000</a>
%H A056793 Angad Singh, <a href="https://doi.org/10.1017/mag.2022.16">Note 106.01, The number of divisors of the LCM of the first n natural numbers</a>, The Mathematical Gazette, Vol. 106, No. 565 (2022), pp. 116-117.
%F A056793 a(n) = d(lcm(1..n)) = A000005(A003418(n)).
%F A056793 a(n) = Product_{prime p <= n} (floor(log(n)/log(p)) + 1). - _Wei Zhou_, Jun 25 2011
%F A056793 a(n) = Product_{k>=1} (1+1/k)^pi(n^(1/k)), where pi(n) = A000720(n) (Singh, 2022). - _Amiram Eldar_, Aug 19 2023
%e A056793 n = 20: lcm(1..20) = 2*2*2*2*3*3*5*7*11*13*17*19 = 232792560 and d(232792560) = 5*3*64 = 960.
%p A056793 A056793 := proc(n)
%p A056793 numtheory[tau](lcm($1..n)) ;
%p A056793 end proc; # _Nathaniel Johnston_, Jun 26 2011
%t A056793 Table[DivisorSigma[0, LCM @@ Range[n]], {n, 50}]
%t A056793 Table[Product[Floor[Log[Prime[i], n]] + 1, {i, PrimePi[n]}], {n, 100}] (* _Wei Zhou_, Jun 25 2011 *)
%o A056793 (PARI) a(n)=n+=.5;prod(e=1,log(n)\log(2),(1+1/e)^primepi(n^(1/e))) \\ _Charles R Greathouse IV_, Jun 06 2013
%o A056793 (Python)
%o A056793 from math import lcm
%o A056793 from sympy import divisor_count
%o A056793 from itertools import accumulate, count, islice
%o A056793 def agen(): yield from map(divisor_count, accumulate(count(1), lcm))
%o A056793 print(list(islice(agen(), 46))) # _Michael S. Branicky_, Jun 25 2022
%Y A056793 Cf. A000005, A000720, A003418, A024619, A101207.
%K A056793 nonn
%O A056793 1,2
%A A056793 _Labos Elemer_, Aug 28 2000