A293893 -id:A293893 - 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");

A293894 Numbers n such that A083722(n) > 1 and A083722(n) occurs earlier in A083722.

Original entry on oeis.org

27, 125, 147, 539, 2197, 2992, 3159, 3249, 3757, 4199, 4851, 5733, 6517, 11774, 15717, 16807, 19652, 20475, 25289, 28899, 30625, 31213, 31465, 33275, 34122, 41327, 43384, 44616, 50255, 60858, 61250, 61750, 62271

Offset: 1

Antti Karttunen, Nov 02 2017

nonn

Equally, numbers n such that A293892(n) > 1 and A293892(n) <= max(A293892(1) .. A293892(n-1)).
Starts like A137800 except that term 3159 is not included in A137800, and furthermore, the latter sequence is not monotonic.
Question: Are there such runs of composites that contain three or more numbers whose largest prime factor is the same prime? In other words, is the intersection of A293893 and A293894 empty or not?

David A. Corneth, Table of n, a(n) for n = 1..101

Cf. A083722, A137800, A293892, A293893.

Flatten@ Values@ Map[Rest, Rest@ PositionIndex@ Array[Times @@ Select[Prime@ Range[#1, #1 + #2], Function[p, p <= #3]] & @@ {PrimePi@ NextPrime[FactorInteger[#][[-1, 1]]], PrimePi@ #, #} &, 10^4]] (* Michael De Vlieger, Nov 03 2017 *)

upto(n) = {my(l = List(), p = 3, res = List, c); forprime(q = 5, nextprime(n + 1), for(i = p + 1, q - 1, f = factor(i)[, 1]; listput(l, [f[#f], precprime(i), i])); p = q); listsort(l); i = 1; while(i < #l - 1, if(l[i][1] == l[i+1][1], if(l[i][2] == l[i+1][2], listput(res, l[i+1][3]))); i++); listsort(res); res} \\ David A. Corneth, Nov 03 2017

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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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A293894 Numbers n such that A083722(n) > 1 and A083722(n) occurs earlier in A083722.

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