A058017 a(n) is the smallest prime > LCM(1,...,x), where x is the n-th prime power (A000961).

2, 3, 7, 13, 61, 421, 853, 2521, 27733, 360391, 720743, 12252259, 232792561, 5354228921, 26771144401, 80313433231, 2329089562843, 72201776446801, 144403552893641, 5342931457063253, 219060189739591279, 9419588158802421659, 442720643463713815201, 3099044504245996706459

Offset

1,1

Comments

For the first 100 prime powers, the difference between a(n) and the LCM is either 1 or a prime.

The values of x are taken to be prime powers so that each distinct LCM occurs exactly once.

Links

Table of n, a(n) for n=1..24.

Formula

a(n) = A151800(A051451(n)) = A051451(n) + A058018(n). - Amiram Eldar, Aug 13 2024

Example

The 6th distinct prime power is A000961(7) = 8, LCM(1,...,8) = 840 and 853 is the first prime that follows, thus a(7) = 853.

Mathematica

With[{max = 50}, NextPrime[Exp[Accumulate[Join[{0}, Select[Array[MangoldtLambda, max], # > 0 &]]]]]] (* Amiram Eldar, Aug 13 2024 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if ((n==1) || isprimepower(n), print1(nextprime(lcm(vector(n, x, x)) + 1), ", "))); } \\ Michel Marcus, Apr 09 2015

Crossrefs

Cf. A000961, A003418, A051451, A058018, A151800.

Sequence in context: A092965 A051454 A051452 * A049536 A065508 A078154

Adjacent sequences: A058014 A058015 A058016 * A058018 A058019 A058020

Keyword

nonn

Author

Labos Elemer, Nov 14 2000

Extensions

Edited by Franklin T. Adams-Watters, Aug 15 2006

Offset changed to 1 and more terms from Michel Marcus, Apr 09 2015

Name corrected by Amiram Eldar, Aug 13 2024

Status

approved