A363956 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of prime(omega(a(n-1))).
1, 2, 4, 6, 3, 8, 10, 9, 12, 15, 18, 21, 24, 27, 14, 30, 5, 16, 20, 33, 36, 39, 42, 25, 22, 45, 48, 51, 54, 57, 60, 35, 63, 66, 40, 69, 72, 75, 78, 50, 81, 26, 84, 55, 87, 90, 65, 93, 96, 99, 102, 70, 80, 105, 85, 108, 111, 114, 95, 117, 120, 100, 123, 126, 110, 115, 129, 132, 125, 28, 135, 138
Offset: 1
Keywords
Examples
a(10) = 15 as prime(omega(a(9))) = prime(A001221(12)) = prime(2) = 3, and 15 is the smallest unused number that is a multiple of 3.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Scott R. Shannon, Image of the first 500000 terms. The green line is a(n) = n.
- Michael De Vlieger, Log log plot of a(n), n = 1..2^20.
- Michael De Vlieger, Log log plot of a(n), n = 1..2^12, showing primes in red, composite prime powers in gold, squarefree composites in green, and numbers neither squarefree nor composite in blue. Powerful numbers that are not prime powers are highlighted in light blue.
Programs
-
Mathematica
nn = 120; c[] := False; m[] := 1; f[x_] := Prime@ PrimeNu[x]; Array[Set[{a[#], c[#], m[#]}, {#, True, 2}] &, 2]; j = 2; Do[k = f[j]; While[c[m[k] k], m[k]++]; k *= m[k]; Set[{a[n], c[k], j}, {k, True, k}], {n, 3, nn}]; Array[a, nn] (* Michael De Vlieger, Jul 01 2023 *)
Comments