A330252 a(1) = 1; for n > 1, a(n) = n*a(n-1) if n is a prime, otherwise a(n) = floor(a(n-1)/A020639(n)), where A020639(n) is the smallest prime divisor of n.

1, 2, 6, 3, 15, 7, 49, 24, 8, 4, 44, 22, 286, 143, 47, 23, 391, 195, 3705, 1852, 617, 308, 7084, 3542, 708, 354, 118, 59, 1711, 855, 26505, 13252, 4417, 2208, 441, 220, 8140, 4070, 1356, 678, 27798, 13899, 597657, 298828, 99609, 49804, 2340788, 1170394, 167199, 83599

Offset: 1

Author

Scott R. Shannon, Dec 07 2019

Keywords

• nonn

Comments

The sequence contains 3291 nonzero terms, after which a(3292) and all subsequent terms equal 0. The largest term is a(1627) = 1739701024619973666776171644354261426018152354833927524.

Examples

			a(3) = 6 as n = 3 is prime and 3 * a(2) = 3 * 2 = 6.
a(4) = 3 as n = 4 is composite with a smallest prime divisor of 2, thus a(4) = floor(a(3)/2) = floor(6/2) = 3.
a(15) = 47 as n = 15 is composite with a smallest prime divisor of 3, thus a(15) = floor(a(14)/3) = floor(143/3) = 47.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..3292.

Crossrefs

Cf. A000040, A020639, A330253.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = If[PrimeQ[n], n*a[n - 1], Floor[a[n - 1] / FactorInteger[n][[1, 1]]]]; Array[a, 50] (* Amiram Eldar, Dec 07 2019 *)