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

Author

Reinhard Zumkeller, May 04 2003

Keywords

• nonn

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

Crossrefs

Cf. A006530, A083721, A083720.

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

Programs

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 *)

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

Formula

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

Extensions

More terms from Michel Marcus, Jun 26 2016