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%I #11 Nov 01 2024 23:55:15
%S 1,4,72,1800,529200,64033200,21643221600,6254891042400,
%T 2258015666306400,17917354312141284000,15068494976510819844000,
%U 28961647344853795740168000,39648495215104846368289992000,66649120456591246745095476552000,123234223724237215231681536144648000,1905570801447880059127491593404692024000
%N a(n) = Product{i = 1..(n-1)} prime(i)^e_i, where prime(i)^e_i is the smallest power of prime(i) which exceeds prime(n).
%C a(n) is the product of powers of primes p, for all p < prime(n), where each prime power is the smallest which exceeds prime(n), (compare with A099795). Every term may be expressed as a product of primorial powers, (A002110(n-1)^2 being the greatest primorial power divisor of a(n)).
%C From _Michael De Vlieger_, Oct 26 2024: (Start)
%C This sequence adds 1 to all exponents of prime power factors of A099795(n) for n > 1.
%C Proper subset of A001694, all terms are powerful. (End)
%H Michael De Vlieger, <a href="/A377356/b377356.txt">Table of n, a(n) for n = 1..193</a>
%F a(n) = A002110(n-1)*A099795(n); A007947(a(n)) = rad(a(n)) = A002110(n-1).
%e For n = 5, a(5) = 529200, since prime(5) = 11, thus we have 2^4*3^3*5^2*7^2 = 16*27*25*49 = 529200. We may express this instead as 210*2520 = A002110(4)*A099795(5) = 210^2*6^1*2^1 = 529200.
%e From _Michael De Vlieger_, Oct 26 2024: (Start)
%e Table of first 12 terms showing exponents of prime power factors of a(n), where "." represents 0.
%e Exponents of primes
%e 1 1 1 1 2 2 3
%e n a(n) 2 3 5 7 1 3 7 9 3 9 1
%e -------------------------------------------------------
%e 1 1 . . . . . . . . . . .
%e 2 4 2 . . . . . . . . . .
%e 3 72 3 2 . . . . . . . . .
%e 4 1800 3 2 2 . . . . . . . .
%e 5 529200 4 3 2 2 . . . . . . .
%e 6 64033200 4 3 2 2 2 . . . . . .
%e 7 21643221600 5 3 2 2 2 2 . . . . .
%e 8 6254891042400 5 3 2 2 2 2 2 . . . .
%e 9 2258015666306400 5 3 2 2 2 2 2 2 . . .
%e 10 17917354312141284000 5 4 3 2 2 2 2 2 2 . .
%e 11 15068494976510819844000 5 4 3 2 2 2 2 2 2 2 .
%e 12 28961647344853795740168000 6 4 3 2 2 2 2 2 2 2 2 (End)
%t Array[Product[Prime[i]^(1 + Floor[Log[Prime[i], Prime[#]]]), {i, # - 1}] &, 12] (* _Michael De Vlieger_, Oct 26 2024 *)
%Y Cf. A000040, A001694, A002110, A007947, A099795.
%K nonn
%O 1,2
%A _David James Sycamore_, Oct 26 2024
%E More terms from _Michael De Vlieger_, Oct 26 2024