

A070536


Number of terms in nth 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
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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

Antti Karttunen, Table of n, a(n) for n = 1..65537


FORMULA

a(n) = A051664(n)  A006530(n).


EXAMPLE

n=21: Cyclotomic[21,x]=1x+x^3x^4+x^6x^8+x^9x^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

Cf. A006530, A051664, A070537, A070776.
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 A030201 A055668
Adjacent sequences: A070533 A070534 A070535 * A070537 A070538 A070539


KEYWORD

nonn


AUTHOR

Labos Elemer, May 03 2002


EXTENSIONS

Data section extended to 105 terms by Antti Karttunen, Sep 10 2018


STATUS

approved



