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A058018
Difference between LCM(1,...,x) and the smallest prime > LCM(1,...,x), where x is the n-th prime power (A000961).
1
1, 1, 1, 1, 1, 1, 13, 1, 13, 31, 23, 19, 1, 41, 1, 31, 43, 1, 41, 53, 79, 59, 1, 59, 61, 113, 97, 179, 73, 73, 97, 103, 101, 109, 1, 229, 109, 139, 113, 227, 131, 191, 163, 1, 199, 151, 139, 1, 223, 229, 367, 239, 499, 251, 509, 251, 227, 373, 281, 233, 283, 229, 277, 263
OFFSET
1,7
COMMENTS
The first value corresponds to x = 1, LCM(1) = 1.
For the first 100 prime powers, the value is either prime or 1.
The values of x are taken to be prime powers so that each distinct LCM occurs exactly once.
FORMULA
a(n) = A013632(A051451(n)) = A058017(n) - A051451(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) = 853-840 = 13.
MATHEMATICA
With[{max = 250}, (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), v = lcm(vector(n, x, x)); print1(nextprime(v+1) - v, ", ")); ); } \\ 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 set to 1 by Michel Marcus, Apr 09 2015
Name corrected by Amiram Eldar, Aug 13 2024
STATUS
approved