A293894 -id:A293894 - cp's OEIS frontend

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

Reinhard Zumkeller, May 04 2003

nonn

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

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

Cf. A006530, A083721, A083720.

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

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 *)

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

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

More terms from Michel Marcus, Jun 26 2016

A293892 Restricted growth sequence transform of A083722.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 5, 6, 1, 7, 1, 8, 9, 10, 1, 11, 1, 12, 13, 14, 1, 15, 16, 17, 15, 18, 1, 19, 1, 20, 21, 22, 23, 24, 1, 25, 26, 27, 1, 28, 1, 29, 30, 31, 1, 32, 33, 34, 35, 36, 1, 37, 38, 39, 40, 41, 1, 42, 1, 43, 44, 45, 46, 47, 1, 48, 49, 50, 1, 51, 1, 52, 53, 54, 55, 56, 1, 57, 58, 59, 1, 60, 61, 62, 63, 64, 1, 65, 66, 67, 68, 69, 70, 71, 1, 72, 73

Offset: 1

Antti Karttunen, Nov 02 2017

nonn

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

Antti Karttunen, Table of n, a(n) for n = 1..65536

Cf. A083722, A293893, A293894.

allocatemem(2^30);
up_to = 65536;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A083722(n) = { if(n==1, return (1)); my(gpf = vecmax(factor(n)[, 1])); my(pp = 1); forprime(p=gpf+1, n, pp *= p; ); pp; } \\ This function from Michel Marcus, Jun 26 2016
write_to_bfile(1,rgs_transform(vector(up_to,n,A083722(n))),"b293892.txt");

A293893 Numbers n such that A083722(n) > 1 and A083722(n) occurs later in A083722.

Original entry on oeis.org

24, 120, 140, 528, 2184, 2975, 3146, 3230, 3740, 4180, 4840, 5720, 6498, 11745, 15686, 16800, 19635, 20449, 25270, 28880, 30618, 31200, 31434, 33264, 34075, 41310, 43355, 44590, 50232, 60835, 61236, 61731, 62234

Offset: 1

Antti Karttunen, Nov 02 2017

nonn

Equally, numbers n such that A293892(n) > 1 and A293892(n) occurs later in A293892.
Starts like A137799 except that term 3146 is not included in A137799, and furthermore, the latter sequence is not monotonic.
See also comments in A293894.

Cf. A083722, A137799, A293892, A293894.

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

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A293892 Restricted growth sequence transform of A083722.

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A293893 Numbers n such that A083722(n) > 1 and A083722(n) occurs later in A083722.

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