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A070537
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Numbers such that the n-th cyclotomic polynomial has more terms than the largest prime factor of n.
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5
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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
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1,2
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COMMENTS
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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
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10001
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FORMULA
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Numbers n satisfying A070536(n) = A051664(n) - A006530(n) > 0.
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EXAMPLE
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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.
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PROG
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(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, ", ")))
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, May 03 2002
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STATUS
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approved
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