A073752 -id:A073752 - cp's OEIS frontend

A073753 a(n) = A073752(A073752(n)), where A073752(n) = gcd(n/spf(n), n/gpf(n)), with spf(n) as the smallest and gpf(n) as the greatest prime factor of n (see A020639, A006530).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 9, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 2

Offset: 1

Reinhard Zumkeller, Aug 07 2002

nonn

a(n) = A062378(n) for n<90, but a(90)=3 <> A062378(90)=1.

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

Cf. A006530, A020639, A073752.

Differs from A062378 for the first time at n=90.

A073752[n_] := With[{f = FactorInteger[n][[All, 1]]}, GCD[n/f[[1]], n/f[[-1]]]];
a[n_] := A073752[A073752[n]];
Array[a, 100] (* Jean-François Alcover, Dec 03 2021 *)

a(n) = A073752(A073752(n)).

Name edited by Antti Karttunen, Sep 23 2017

A087653 Maximum difference between exponents in n-th cyclotomic polynomial.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 2, 8, 1, 3, 1, 2, 2, 1, 1, 4, 5, 1, 9, 2, 1, 2, 1, 16, 2, 1, 4, 6, 1, 1, 2, 4, 1, 2, 1, 2, 6, 1, 1, 8, 7, 5, 2, 2, 1, 9, 4, 4, 2, 1, 1, 4, 1, 1, 6, 32, 4, 2, 1, 2, 2, 4, 1, 12, 1, 1, 10, 2, 6, 2, 1, 8, 27, 1, 1, 4, 4, 1, 2, 4, 1, 6, 6, 2, 2, 1, 4

Offset: 1

Ralf Stephan, Sep 25 2003

Differs from A000190, A003557, A073752.

			Cyc(9) = x^6 + x^3 + x^0, so a(9) = 3.

Michel Marcus, Table of n, a(n) for n = 1..5000
Ala'a Al-Kateeb, Mary Ambrosino, Hoon Hong, and Eunjeong Lee, Maximum gap in cyclotomic polynomials, arXiv:1911.11667 [math.NT], 2019.
Hoon Hong, Eunjeong Lee, Hyang-Sook Lee, Cheol-Min Park, Maximum Gap in (Inverse) Cyclotomic Polynomial, arXiv:1101.4255 [math.NT], 2011.

Cf. A013595.

a[n_] := Max[Differences[Exponent[Cyclotomic [n, x], x, List]]] (* Jonathan Sondow, Jan 09 2014 *)

{ mtermgap(pol)=local(p, m); m=0; p=0; for(k=0, poldegree(pol), if(polcoeff(pol, k)!=0, if(m

a(p) = a(p*q) = p-1 for primes p < q (by Hong et al.). - Jonathan Sondow, Jan 09 2014

cp's OEIS Frontend

A073753 a(n) = A073752(A073752(n)), where A073752(n) = gcd(n/spf(n), n/gpf(n)), with spf(n) as the smallest and gpf(n) as the greatest prime factor of n (see A020639, A006530).

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