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Search: id:A137818
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| A137818 |
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Non-biquadratefree "year numbers": phi(n) = 2 phi(sigma(n)) and p^4 | n for some p>1. |
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2
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| 295569, 1811079, 1964375, 2069469, 4473387, 5854375, 10936053, 13260625, 18029709, 21576537, 22182093, 25536875, 35595625, 46404333, 49648383, 55094375, 57044817, 58650625, 67009923, 69166467, 72681875, 76106875
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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See A137815 for general comments and references about "year numbers". This is the subsequence of elements of A137815 divisible by a biquadrateful number, i.e. its intersection with A046101 (numbers divisible by the 4th power of some prime). As such, it is of course also a subsequence of A137817 and a fortiori of A137816.
There are only 28 such numbers below 10^8.
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PROGRAM
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(PARI) for( i=1, #A137816, vecmax( factor( A137816[i])[, 2])>3 && print1(A137816[i]", "))
(PARI) for( i=1, #A046099, eulerphi(A046099[i])==2*eulerphi(sigma(A046099[i])) && print1( A046099[i] ", "))
(PARI) for( n=1, 10^9, issquarefree(n) && next; vecmax(factor(n)[, 2])>3 || next; eulerphi(n)==2*eulerphi(sigma(n)) && print1(n", "))
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CROSSREFS
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Cf. A137815-A137819, A046101.
Sequence in context: A023351 A109031 A137817 this_sequence A164946 A048906 A119740
Adjacent sequences: A137815 A137816 A137817 this_sequence A137819 A137820 A137821
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KEYWORD
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nonn
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AUTHOR
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Richard K. Guy (rkg(AT)cpsc.ucalgary.ca), Richard J. Mathar (mathar(AT)strw.leidenuniv.nl) and M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 11 2008
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