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Search: id:A144695
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| A144695 |
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Numbers n such that sigma_1(n)/sigma_0(n) = c^2, c an integer. |
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1
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| 1, 7, 17, 22, 30, 31, 71, 94, 97, 115, 119, 127, 138, 154, 164, 165, 199, 210, 214, 217, 241, 260, 265, 318, 337, 343, 374, 382, 449, 497, 510, 513, 517, 527, 577, 647, 658, 668, 679, 682, 705, 745, 759, 805, 862, 881, 889, 894, 930, 966, 967, 996, 1102, 1125
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A000203(n)/A000005(n) = c^2. Generalized sigma-sequences are sequences of numbers n for which sigma_r(n)/sigma_s(n) = c^t . Sigma_i(n) denotes sum of i-th powers of divisors of n; c,r,s,t positive integers. This sequence has r=1,s=0,t=2, sequence A003601 has r=1,s=0,t=1, sequence {1,21,53,85,102,110,127,217,431,....} has r=1,s=0,t=3, sequence A020487 has r=2,s=1,t=1, sequence A020486 has r=2,s=0,t=1, sequence A140480 has r=2,s=0,t=2.
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LINKS
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Divisor function
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MAPLE
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A000005 := proc(n) numtheory[tau](n) ; end: A000203 := proc(n) numtheory[sigma](n) ; end: isA144695 := proc(n) local s ; s := A000005(n) ; if s <> 0 then issqr(A000203(n)/s) ; else false ; fi; end: for n from 1 to 5000 do if isA144695(n) then printf("%d, ", n) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2008]
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CROSSREFS
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Cf. A000005, A000203, A140480, A003601, A020487, A020486
Sequence in context: A155774 A104480 A053746 this_sequence A125244 A070416 A087168
Adjacent sequences: A144692 A144693 A144694 this_sequence A144696 A144697 A144698
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KEYWORD
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easy,nonn
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AUTHOR
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Ctibor O. Zizka (c.zizka(AT)seznam.cz), Sep 19 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2008
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