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Search: id:A097318
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| A097318 |
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Numbers with more than one prime factor and, in the ordered factorization, the exponent never increases when read from left to right. |
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+0
4
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| 6, 10, 12, 14, 15, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 51, 52, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 102, 104, 105, 106, 110, 111, 112, 114
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If n = Sum[k=1..m, p(k)^e(k)], then k>1, e(1) >= e(2) >=...>= e(m).
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LINKS
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S. Ramanujan, Asymptotic formulae for the distribution of integers of various types, Proc. London Math. Soc. 2, 16 (1917), 112-132.
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EXAMPLE
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60 is 2^2*3^1*5^1, A001221(60)=3 and 2>=1>=1, so 60 is in sequence.
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PROGRAM
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(PARI) for(n=1, 130, F=factor(n):t=0:s=matsize(F)[1]: if(s>1, for(k=1, s-1, if(F[k, 2]<F[k+1, 2], t=1:break)): if(!t, print1(n", "))))
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CROSSREFS
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Subset of A024619. Cf. A097319, A097320.
Sequence in context: A069059 A139587 A119313 this_sequence A080363 A082300 A050703
Adjacent sequences: A097315 A097316 A097317 this_sequence A097319 A097320 A097321
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 04 2004
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