The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A070536 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A070536

Number of terms in n-th cyclotomic polynomial minus largest prime factor of n; a(1)=1 by convention.
(history; published version)

#20 by Susanna Cuyler at Tue Sep 11 17:02:28 EDT 2018

STATUS

proposed

approved

#19 by Antti Karttunen at Mon Sep 10 21:40:00 EDT 2018

STATUS

editing

proposed

#18 by Antti Karttunen at Mon Sep 10 21:39:48 EDT 2018

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 (with , as A051664) which 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

STATUS

proposed

editing

#17 by Michael De Vlieger at Mon Sep 10 21:37:02 EDT 2018

STATUS

editing

proposed

#16 by Michael De Vlieger at Mon Sep 10 21:37:01 EDT 2018

MATHEMATICA

Array[Length@ Cyclotomic[#, x] - FactorInteger[#][[-1, 1]] &, 105] (* Michael De Vlieger, Sep 10 2018 *)

STATUS

proposed

editing

#15 by Antti Karttunen at Mon Sep 10 21:12:12 EDT 2018

STATUS

editing

proposed

#14 by Antti Karttunen at Mon Sep 10 21:12:04 EDT 2018

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 (with A051664) which 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

STATUS

proposed

editing

#13 by Antti Karttunen at Mon Sep 10 21:11:28 EDT 2018

STATUS

editing

proposed

#12 by Antti Karttunen at Mon Sep 10 21:11:24 EDT 2018

PROG

A051664(n) = length(select(x->x!=0, Vec(polcyclo(n)))); \\ After program from From A051664

STATUS

proposed

editing

#11 by Antti Karttunen at Mon Sep 10 21:08:03 EDT 2018

STATUS

editing

proposed