A250302
Positive integers k whose square is, for some prime p, the largest integer m such that both m and m-1 factor into primes less than or equal to p.
Original entry on oeis.org
3, 9, 99, 351, 13311, 1205645, 138982582999
Offset: 1
Here are the largest pairs of consecutive integers with prime factors p or smaller:
p : pair
--------------------------
3 : 3^2-1 and 3^2;
5 : 9^2-1 and 9^2;
11 : 99^2-1 and 99^2;
13 : 351^2-1 and 351^2;
29 : 13311^2-1 and 13311^2;
53 : 1205645^2-1 and 1205645^2;
103 : 138982582999^2-1 and 138982582999^2.
-
lista(v_002072) = {v = v_002072; for (i=1, #v, vi = v[i]; if (issquare(vi+1), print1(sqrtint(vi+1), ", ")););} \\ Michel Marcus, Feb 28 2015
A303339
a(n) is the largest triangular number that is prime(n)-smooth.
Original entry on oeis.org
1, 36, 3240, 9568125, 48024900, 7589181600, 56495217870, 70320436841655, 70320436841655, 15696858221890560, 1298157862542190650, 5996877118268400000, 2043364250317598208000, 88678944280899462664980, 615491489313111203244375, 1056447213455901684717300
Offset: 1
The first prime is 2, and the only triangular number that is 2-smooth is 1, so a(1) = 1.
The second prime is 3, and the only triangular numbers that are 3-smooth are 1, 3, 6 = 2 * 3, and 36 = 2^2 * 3^2, so a(2) = 2.
The third prime is 5, and the only triangular numbers that are 5-smooth are the 3-smooth triangular numbers and 10 = 2 * 5, 15 = 3 * 5, 45 = 3^2 * 5, 120 = 2^3 * 3 * 5, 300 = 2^2 * 3 * 5^2, and 3240 = 2^3 * 3^4 * 5, so a(3) = 3240.
Comments