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A064607
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Partial sum of Sigma_4(n) is divisible by n, where Sigma_4(n)=A001159(n).
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7
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1, 2, 7, 151, 257, 1823, 3048, 5588, 6875, 7201, 8973, 24099, 5249801, 9177919, 18926164, 70079434, 78647747, 705686794
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Analogous sequences for various arithmetical functions are A050226, A056650, A064605-A064607, A064610, A064611, A048290, A062982, A045345.
a(19) > 2*10^9. [From Donovan Johnson, Jun 21 2010]
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FORMULA
| Mod[Sum{sigma_4(j), j=1..n}, n]=Mod[A064604(n), n]=0
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EXAMPLE
| Adding 4th-power divisor-sums for j=1,...,7 gives 1+17+82+273+626+1394+2402=4795 which is divisible by n=7, so 7 is here and the integer quotient is 655.
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MATHEMATICA
| k = 1; lst = {}; s = 0; While[k < 1000000001, s = s + DivisorSigma[4, k]; If[ Mod[s, k] == 0, AppendTo[lst, k]; Print@ k]; k++]; lst (*Robert G.Wilson v, Aug 25 2011*)
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CROSSREFS
| A001159, A064604 A050226, A056650, A064605-A064607, A064610-A064612, A048290, A062982, A045345.
Sequence in context: A201172 A062617 A207139 * A182974 A005345 A174366
Adjacent sequences: A064604 A064605 A064606 * A064608 A064609 A064610
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Sep 24 2001
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EXTENSIONS
| a(13)-a(18) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jun 21 2010
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