A051454 a(n) is the smallest prime factor of 1 + lcm(1..k) where k is the n-th prime power A000961(n).

2, 3, 7, 13, 61, 421, 29, 2521, 19, 89, 71, 1693, 232792561, 6659, 26771144401, 331, 101, 72201776446801, 1801, 173, 54941, 89, 442720643463713815201, 593, 5171, 239, 1222615931, 103, 7265496855919, 6562349363, 4447, 147099357127, 1931

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..82

Example

1 + lcm(1..8) = 29^2, so its smallest prime divisor is 29; it occurs as the 7th term in the sequence because 8 is the 7th prime power: A000961(7) = 8.

Prog

(Magma) a:=[]; lcm:=1; for k in [1..83] do if (k eq 1) or IsPrimePower(k) then lcm:=Lcm(lcm, k); a:=a cat [Factorization(1+lcm)[1][1]]; end if; end for; a; // Jon E. Schoenfield, May 28 2018
(PARI) a(n) = {my(nb = 1, lc = 1, k = 2); while (nb != n, if (isprimepower(k), nb++; lc = lcm(lc, k)); k++; ); vecmin(factor(lc +1)[, 1]); } \\ Michel Marcus, May 29 2018

Crossrefs

Cf. A000961, A003418, A049536, A049537, A051301, A051342, A051452.

Sequence in context: A092969 A089136 A092965 * A051452 A058017 A049536

Adjacent sequences: A051451 A051452 A051453 * A051455 A051456 A051457

Keyword

nonn

Author

Labos Elemer

Status

approved