A330252 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A000040, A020639, A330253.

Sequence in context: A072155 A094299 A304537 * A368823 A372000 A121566

Adjacent sequences: A330249 A330250 A330251 * A330253 A330254 A330255

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Dec 07 2019

STATUS

approved