A083260 -id:A083260 - cp's OEIS frontend

A083258 a(n) = gcd(A046523(n), n).

1, 2, 1, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 3, 16, 1, 6, 1, 4, 3, 2, 1, 24, 1, 2, 1, 4, 1, 30, 1, 32, 3, 2, 1, 36, 1, 2, 3, 8, 1, 6, 1, 4, 3, 2, 1, 48, 1, 2, 3, 4, 1, 6, 1, 8, 3, 2, 1, 60, 1, 2, 3, 64, 1, 6, 1, 4, 3, 10, 1, 72, 1, 2, 3, 4, 1, 6, 1, 16, 1, 2, 1, 12, 1, 2, 3, 8, 1, 30, 1, 4, 3, 2, 1, 96, 1, 2

Offset: 1

Labos Elemer, May 09 2003

nonn

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

Cf. A046523, A071364, A083255-A083260, A083261.

Table[GCD[n, Times @@ MapIndexed[Prime[First[#2]]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]]], {n, 98}] (* Michael De Vlieger, May 21 2017 *)

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
A083258(n) = gcd(n,A046523(n)); \\ Antti Karttunen, May 21 2017

A083259 a(n) = gcd(n, A071364(n)), where A071364(n) is the smallest number with same sequence of exponents in canonical prime factorization as n.

Original entry on oeis.org

1, 2, 1, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 3, 16, 1, 18, 1, 4, 3, 2, 1, 24, 1, 2, 1, 4, 1, 30, 1, 32, 3, 2, 1, 36, 1, 2, 3, 8, 1, 6, 1, 4, 3, 2, 1, 48, 1, 2, 3, 4, 1, 54, 1, 8, 3, 2, 1, 60, 1, 2, 3, 64, 1, 6, 1, 4, 3, 10, 1, 72, 1, 2, 3, 4, 1, 6, 1, 16, 1, 2, 1, 12, 1, 2, 3, 8, 1, 90, 1, 4, 3, 2, 1, 96, 1

Offset: 1

Labos Elemer, May 09 2003

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A007395, A002808, A046523, A071364, A083255-A083260, A322361, A330749.

A071364(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 1] = prime(i)); factorback(f); }; \\ From A071364
A083259(n) = gcd(A071364(n),n); \\ Antti Karttunen, Jan 22 2020

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

A083258 a(n) = gcd(A046523(n), n).

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A083259 a(n) = gcd(n, A071364(n)), where A071364(n) is the smallest number with same sequence of exponents in canonical prime factorization as n.

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PARI

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

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PARI