A058017 -id:A058017 - cp's OEIS frontend

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, 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

Labos Elemer, Nov 14 2000

nonn

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.

			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.

Cf. A000961, A003418, A013632, A051451, A058017.

With[{max = 250}, (NextPrime[#] - #)& /@ Exp[Accumulate[Join[{0}, Select[Array[MangoldtLambda, max], # > 0 &]]]]] (* Amiram Eldar, Aug 13 2024 *)

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

a(n) = A013632(A051451(n)) = A058017(n) - A051451(n). - Amiram Eldar, Aug 13 2024

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

cp's OEIS Frontend

A058018 Difference between LCM(1,...,x) and the smallest prime > LCM(1,...,x), where x is the n-th prime power (A000961).

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