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Search: id:A046764
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| A046764 |
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Sum of the 4th powers of the divisors of n is divisible by n. |
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+0
3
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| 1, 34, 84, 156, 364, 492, 1092, 3444, 5617, 6396, 11234, 22468, 33628, 44772, 67404, 100884, 157276, 190978, 292084, 435708, 437164, 471828, 549687, 569772, 709937, 742612, 763912, 876252, 986076, 1099374, 1118480, 1289484, 1311492, 1419874
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OFFSET
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1,2
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COMMENT
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Compare with multiply perfect numbers, A007691. Here Sum[ divisors ] is replaced by Sum[ 4th powers of divisors ].
Problem 11090 proves that this sequence is infinite. - T. D. Noe (noe(AT)sspectra.com), Apr 18 2006
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REFERENCES
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Florian Luca, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113 (2006), 372-373.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
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FORMULA
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Mod[ Sigma [ 4, n ], n ]=0
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EXAMPLE
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a[ 3 ]=n=84, Sigma[ 4,84 ]=Sum(d^4)=53771172=640133*84=640133*n a[ 9 ]=n=5617 with Sigma[ 4,5617 ]=995446331475844=5617*17722083332, a multiple of n.
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MATHEMATICA
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Do[If[Mod[DivisorSigma[4, n], n]==0, Print[n]], {n, 1, 2*10^6}]
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CROSSREFS
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Cf. A007691.
Sequence in context: A066284 A036199 A092223 this_sequence A086005 A140602 A067977
Adjacent sequences: A046761 A046762 A046763 this_sequence A046765 A046766 A046767
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 09 2000
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