A381675 a(n) = p*2^(p - 1)*(p - 1)!, where p = prime(n).
4, 24, 1920, 322560, 40874803200, 25505877196800, 23310331287699456000, 31888533201572855808000, 108431217215972213061058560000, 2373442412632986039472006832848896000000, 8829205774994708066835865418197893120000000, 945837910352576904120619801361499836578686566400000000
Offset: 1
Examples
Table of n, A100484(n), and a(n) for n = 1..12, showing prime power decomposition via a list of exponents of prime factors:
Exponents of prime factors:
1 1 1 1 2 2 3 3
n 2*prime(n) a(n) 2 3 5 7 1 3 7 9 3 9 1 7
----------------------------------------------------------
1 4 4 2
2 6 24 3. 1
3 10 1920 7. 1.1
4 14 322560 10. 2.1.1
5 22 40874803200 18. 4.2.1.1
6 26 25505877196800 22. 5.2.1.1.1
7 34 23310331287699456000 31. 6.3.2.1.1.1
8 38 34. 8.3.2.1.1.1.1
9 46 41. 9.4.3.2.1.1.1.1
10 58 53.13.6.4.2.2.1.1.1.1
11 62 56.14.7.4.2.2.1.1.1.1.1
12 74 70.17.8.5.3.2.2.1.1.1.1.1
----------------------------------------------------------
1 1 1 1 2 2 3 3
2 3 5 7 1 3 7 9 3 9 1 7
a(1) = 4 = 2*2.
a(2) = 24 = (2*4) * 3.
a(3) = 1920 = (2*4*6*8) * 5.
a(4) = 322560 = (2*4*6*8*10*12) * 7, etc.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..79
Programs
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Mathematica
Table[p = Prime[n]; p*2^(p - 1)*(p - 1)!, {n, 12}]
Formula
a(n) = Product_{p|k} Product_{m=1..k/p-1} m*p, where k = 2*prime(n).
gpf(a(n)) = prime(n).
Comments