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Search: id:A076361
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| A076361 |
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Numbers n such that d(sigma(n)) = sigma(d(n)) |
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+0
6
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| 1, 3, 44, 49, 66, 68, 70, 76, 99, 121, 124, 147, 153, 164, 169, 170, 171, 172, 243, 245, 268, 275, 279, 361, 363, 387, 425, 475, 507, 529, 564, 603, 620, 644, 652, 724, 775, 841, 844, 845, 873, 891, 927, 948, 961, 964, 1075, 1083, 1132, 1324, 1348, 1377
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)=Commutator[sigma,tau]=0; Solutions to A076360[x]=0.
Assuming Schinzel's hypothesis is true, the sequence is infinite. That conjecture implies that there are infinitely many primes p for which (p^2+p+1)/3 is prime. (E.g. p = 7, 13, 19, 31, 43, 73, 97, ...) For such p, we have d(sigma(p^2)) = d(p^2+p+1) = 4 and sigma(d(p^2)) = sigma(3) = 4, so p^2 is in the sequence. - Dean Hickerson, Jan 24 2006
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LINKS
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Eric Weisstein's World of Mathematics, Schinzel's hypothesis
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MATHEMATICA
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d0[x_] := DivisorSigma[0, x] d1[x_] := DivisorSigma[1, x] Do[s=d0[d1[n]]-d1[d0[n]]; If[s==0, Print[n]], {n, 1, 10000}]
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CROSSREFS
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Cf. A000005, A000203.
Sequence in context: A136648 A114337 A009720 this_sequence A130408 A133073 A055539
Adjacent sequences: A076358 A076359 A076360 this_sequence A076362 A076363 A076364
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KEYWORD
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easy,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 08 2002
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