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A070776
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Numbers k such that number of terms in the k-th cyclotomic polynomial is equal to the largest prime factor of k.
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20
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2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 58, 59, 61, 62, 64, 67, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83, 86, 88, 89, 92, 94, 96, 97, 98, 100
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OFFSET
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1,1
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COMMENTS
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This is also numbers in the form of 2^i*p^j, i >= 0 and j >= 0, p is an odd prime number. - Lei Zhou, Feb 18 2012
From Zhou's formulation (where the exponents i and j should actually have been specified as i > 0 OR j > 0, to exclude 1) it follows that this is a subsequence of A324109. It also follows that A005940(a(n)) = A324106(a(n)) for all n >= 1. - Antti Karttunen, Feb 15 2019
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LINKS
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EXAMPLE
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n=10: Cyclotomic[10,x]=1-x+x^2-x^3+x^4 with 5 terms [including 1] which equals largest prime factor (5) of 10=n.
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MATHEMATICA
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Select[Range[1000], (a=FactorInteger[#]; b=Length[a]; (b==1)||((b==2)&&(a[[1]][[1]]==2)))&] (* Lei Zhou, Feb 18 2012 *)
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PROG
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(PARI)
A051664(n) = length(select(x->x!=0, Vec(polcyclo(n)))); \\ After program in A051664
k=0; n=0; while(k<10000, n++; if(isA070776(n), k++; write("b070776.txt", k, " ", n)));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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