A083722 Product of primes greater than the greatest prime factor of n but not greater than n.

1, 1, 1, 3, 1, 5, 1, 105, 35, 7, 1, 385, 1, 143, 1001, 15015, 1, 85085, 1, 323323, 46189, 4199, 1, 37182145, 7436429, 7429, 37182145, 1062347, 1, 215656441, 1, 100280245065, 86822723, 392863, 955049953, 33426748355, 1, 765049, 247110827, 247357937827, 1, 1448810778701, 1

Offset

1,4

Comments

a(n) = 1 iff n is prime or n is 1.

Apart from 1-terms, the other duplicated terms are: a(24) = a(27), a(120) = a(125), a(140) = a(147), a(528) = a(539), etc, whose positions are listed by A293893 and A293894. - Antti Karttunen, Nov 01 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..2001

Formula

a(n) = A002110(A049084(A007917(n)))/A002110(A049084(A006530(n))).

Mathematica

Array[Times @@ Select[Prime@ Range[#1, #1 + #2], Function[p, p <= #3]] & @@ {PrimePi@ NextPrime[FactorInteger[#][[-1, 1]]], PrimePi@ #, #} &, 43] (* Michael De Vlieger, Nov 01 2017 *)

Prog

(PARI) a(n) = {if (n==1, return (1)); my(gpf = vecmax(factor(n)[, 1])); my(pp = 1); forprime(p=gpf+1, n, pp *= p; ); pp; } \\ Michel Marcus, Jun 26 2016

Crossrefs

Cf. A006530, A083721, A083720.

Cf. A293892 (restricted growth sequence transform), A293893, A293894.

Sequence in context: A166086 A232101 A176249 * A111426 A100576 A212332

Adjacent sequences: A083719 A083720 A083721 * A083723 A083724 A083725

Keyword

nonn

Author

Reinhard Zumkeller, May 04 2003

Extensions

More terms from Michel Marcus, Jun 26 2016

Status

approved