A083256 -id:A083256 - cp's OEIS frontend

A083257 a(n) = A071364(n-th nonprime number) = A071364(A018252(n)).

1, 4, 6, 8, 4, 6, 12, 6, 6, 16, 18, 12, 6, 6, 24, 4, 6, 8, 12, 30, 32, 6, 6, 6, 36, 6, 6, 24, 30, 12, 12, 6, 48, 4, 18, 6, 12, 54, 6, 24, 6, 6, 60, 6, 12, 64, 6, 30, 12, 6, 30, 72, 6, 18, 12, 6, 30, 48, 16, 6, 60, 6, 6, 6, 24, 90, 6, 12, 6, 6, 6, 96, 18, 12, 36, 30, 24, 30, 6, 108, 30, 6

Offset: 1

Labos Elemer, May 09 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A007395, A000040, A002808, A018252, A046523, A071364, A083256.

f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Times @@ (Prime[Range[Length[e]]]^e)]; f[1] = 1; f /@ Select[Range[120], !PrimeQ[#] &] (* Amiram Eldar, Feb 22 2025 *)

Corrected by Ray Chandler, Aug 01 2004

A083260 a(n) = gcd(A046523(n), A071364(n)).

Original entry on oeis.org

1, 2, 2, 4, 2, 6, 2, 8, 4, 6, 2, 12, 2, 6, 6, 16, 2, 6, 2, 12, 6, 6, 2, 24, 4, 6, 8, 12, 2, 30, 2, 32, 6, 6, 6, 36, 2, 6, 6, 24, 2, 30, 2, 12, 12, 6, 2, 48, 4, 6, 6, 12, 2, 6, 6, 24, 6, 6, 2, 60, 2, 6, 12, 64, 6, 30, 2, 12, 6, 30, 2, 72, 2, 6, 6, 12, 6, 30, 2, 48, 16, 6, 2, 60, 6, 6, 6, 24, 2, 30, 6

Offset: 1

Labos Elemer, May 09 2003

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A046523, A071364, A083255, A083256, A083257, A083258, A083259, A083261.

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A071364(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = prime(i)); factorback(f); }; \\ This function from Michel Marcus, Jun 13 2014
A083260(n) = gcd(A046523(n), A071364(n)); \\ Antti Karttunen, Aug 24 2017

A083261 a(n) = gcd(A046523(n+1), A046523(n)).

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 6, 6, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 6, 6, 2, 2, 2, 2, 12, 6, 2, 2, 4, 4, 6, 6, 2, 2, 6, 6, 6, 6, 2, 2, 2, 2, 6, 4, 2, 6, 2, 2, 6, 6, 2, 2, 2, 2, 6, 12, 6, 6, 2, 2, 16, 2, 2, 2, 6, 6, 6, 6, 2, 2, 6, 6, 6, 6, 6, 6, 2, 2, 12, 12, 2, 2, 2, 2

Offset: 1

Labos Elemer, May 09 2003

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A046523, A071364, A083255, A083256, A083257, A083258, A083259, A083260, A286255.

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A083261(n) = gcd(A046523(n),A046523(1+n)); \\ From Antti Karttunen, May 21 2017

cp's OEIS Frontend

A083257 a(n) = A071364(n-th nonprime number) = A071364(A018252(n)).

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A083260 a(n) = gcd(A046523(n), A071364(n)).

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A083261 a(n) = gcd(A046523(n+1), A046523(n)).

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