Original entry on oeis.org
0, 1, 5, 11, 59, 419, 839, 2519, 27719, 360359, 720719, 12252239, 232792559, 5354228879, 26771144399, 80313433199, 2329089562799, 72201776446799, 144403552893599, 5342931457063199, 219060189739591199, 9419588158802421599, 442720643463713815199
Offset: 1
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import Data.List (nub)
a208768 n = a208768_list !! (n-1)
a208768_list = nub a070198_list
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from math import prod
from sympy import primepi, integer_nthroot, integer_log, primerange
def A208768(n):
def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x,k)[0]) for k in range(1,x.bit_length())))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return prod(p**integer_log(m, p)[0] for p in primerange(m+1))-1 # Chai Wah Wu, Aug 15 2024
A051454
a(n) is the smallest prime factor of 1 + lcm(1..k) where k is the n-th prime power A000961(n).
Original entry on oeis.org
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 + 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.
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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
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Join[{2},With[{ppwr=Select[Range[200],PrimePowerQ]},Table[FactorInteger[LCM@@Take[ ppwr,n]+ 1][[1,1]],{n,40}]]] (* Harvey P. Dale, May 28 2024 *)
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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
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from math import prod
from sympy import primepi, integer_nthroot, integer_log, primerange, primefactors
def A051454(n):
def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x,k)[0]) for k in range(1,x.bit_length())))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return min(primefactors(1+prod(p**integer_log(m, p)[0] for p in primerange(m+1)))) # Chai Wah Wu, Aug 15 2024
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