A073818 a(n) = max(prime(i)*(n+1-i) | 1 <= i <= n).

2, 4, 6, 10, 15, 22, 33, 44, 55, 68, 85, 102, 119, 145, 174, 203, 232, 261, 296, 333, 370, 410, 451, 492, 533, 590, 649, 708, 767, 826, 885, 944, 1005, 1072, 1139, 1207, 1278, 1358, 1455, 1552, 1649, 1746, 1843, 1940, 2037, 2134, 2231, 2328, 2425, 2540, 2667

Offset: 1

Author

David Wasserman, Aug 13 2002

Keywords

• easy
• nonn

Comments

Smallest m such that m! is divisible by product_{k=0..n} A002110(k).

Conjecture: define an operator P(n) which when applied to a sequence s(1),s(2),s(3),... leaves s(1),...,s(n) fixed and 1) sorts in descending order if n is prime; or 2) sorts in ascending order if n is not prime every n consecutive terms thereafter. Apply P(2) to 1,2,3,... to get PS(2), then apply P(3) to PS(2) to get PS(3), then apply P(4) to PS(3), etc. The limit of PS(n) is b(n). Let c(n) = b(A000040(n) + 1), then a(n) = c(n-1) for n > 1 with a single exception at n = 5. - Mikhail Kurkov, May 11 2022

Examples

			For n = 5, we take the first 5 primes in ascending order and multiply them by the numbers from 5 to 1 in descending order: 2*5 = 10 3*4 = 12 5*3 = 15 7*2 = 14 11*1 = 11. The largest product is 15, so a(5) = 15.
		

Crossrefs

Cf. A073819, A073820.

Programs

PARI

a(n) = {ret = 0; for (i=1, n, ret = max (ret, prime(i)*(n+1-i));); return (ret);} \\ Michel Marcus, Jun 16 2013

Extensions

Thanks to Naohiro Nomoto for correcting an editing error, Jun 01 2003