login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A070536
Number of terms in n-th cyclotomic polynomial minus largest prime factor of n; a(1)=1 by convention.
4
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 10, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 6, 0, 0, 2, 0, 0, 2, 0, 18, 4, 0, 0, 8, 10, 0, 0, 0, 0, 2, 0, 20, 4, 0, 0, 0, 0, 0, 2, 24, 0, 10, 0, 0, 2, 10, 0, 10, 0, 12, 0, 0, 0, 4, 0, 0, 6, 0, 0, 26
OFFSET
1,15
COMMENTS
When (as at n=105) coefficients are not equal 1 or -1 then terms in C[n,x] are counted with multiplicity. - This is the comment by the original author. However, the claim contradicts the given formula, as A051664 counts each nonzero coefficient just once, regardless of its value. For the version summing the absolute values of the coefficients (thus "with multiplicity"), see A318886. - Antti Karttunen, Sep 10 2018
LINKS
FORMULA
a(n) = A051664(n) - A006530(n).
EXAMPLE
n=21: Cyclotomic[21,x]=1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12 has 9 terms while largest prime factor of 21 is 7
MATHEMATICA
Array[Length@ Cyclotomic[#, x] - FactorInteger[#][[-1, 1]] &, 105] (* Michael De Vlieger, Sep 10 2018 *)
PROG
(PARI)
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1); \\ From A006530.
A051664(n) = length(select(x->x!=0, Vec(polcyclo(n)))); \\ From A051664
A070536(n) = (A051664(n) - A006530(n)); \\ Antti Karttunen, Sep 10 2018
CROSSREFS
Differs from A318886 for the first time at n=105, where a(105) = 26, while A318886(105) = 28.
Sequence in context: A151756 A112053 A089798 * A318886 A369873 A030201
KEYWORD
nonn
AUTHOR
Labos Elemer, May 03 2002
EXTENSIONS
Data section extended to 105 terms by Antti Karttunen, Sep 10 2018
STATUS
approved