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