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

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..51.

Example

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.

Prog

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

Crossrefs

Cf. A073819, A073820.

Sequence in context: A073470 A086182 A035294 * A342091 A239288 A306145

Adjacent sequences: A073815 A073816 A073817 * A073819 A073820 A073821

Keyword

easy,nonn

Author

David Wasserman, Aug 13 2002

Extensions

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

Status

approved