

A070537


Numbers such that the nth cyclotomic polynomial has more terms than the largest prime factor of n.


5



1, 15, 21, 30, 33, 35, 39, 42, 45, 51, 55, 57, 60, 63, 65, 66, 69, 70, 75, 77, 78, 84, 85, 87, 90, 91, 93, 95, 99, 102, 105, 110, 111, 114, 115, 117, 119, 120, 123, 126, 129, 130, 132, 133, 135, 138, 140, 141, 143, 145, 147, 150, 153, 154, 155, 156, 159, 161, 165
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OFFSET

1,2


COMMENTS

When (as at n=105) coefficients are not equal to 1 or 1, terms in C[n,x] are counted with multiplicity.  The comment left by the original author, but please see my comment in A070536.  Antti Karttunen, Feb 15 2019
Union of A324110 and A324111.  Antti Karttunen, Feb 15 2019


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10001


FORMULA

Numbers n satisfying A070536(n) = A051664(n)  A006530(n) > 0.


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 the largest prime factor of 21 is 7; 9 > 7, so 21 is in the sequence.


PROG

(PARI)
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1); \\ From A006530.
A051664(n) = length(select(x>x!=0, Vec(polcyclo(n)))); \\ After program in A051664
isA070537(n) = (A051664(n) > A006530(n)); \\ Antti Karttunen, Feb 15 2019
for(n=1, 165, if(isA070537(n), print1(n, ", ")))


CROSSREFS

Cf. A006530, A051664, A070536, A070776 (complement), A324110, A324111.
Sequence in context: A026048 A195527 A047200 * A324110 A285800 A184041
Adjacent sequences: A070534 A070535 A070536 * A070538 A070539 A070540


KEYWORD

nonn


AUTHOR

Labos Elemer, May 03 2002


STATUS

approved



