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A064605
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Partial sum of Sigma_2(n) is divisible by n, where Sigma_2(n)=A001157(n).
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7
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1, 2, 8, 74, 146, 150, 158, 307, 526, 541, 16157, 20289, 271343, 953614, 1002122, 2233204, 3015123, 15988923, 48033767
(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, A064606, A064607, A064610, A064611, A048290, A062982, A045345.
a(20) > 2*10^9. [From Donovan Johnson, Jun 21 2010]
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FORMULA
| Mod[Sum{sigma_2(j), j=1..n}, n]=Mod[A064602(n), n]=0
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EXAMPLE
| Summarizing divisor-square sums for j=1,...,8 gives 1+5+10+21+26+50+50+85=248, which is divisible by n=8, so 8 is here and the integer quotient is 31.
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MATHEMATICA
| k = 1; lst = {}; s = 0; While[k < 1000000001, s = s + DivisorSigma[2, k]; If[ Mod[s, k] == 0, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G. Wilson v, Apr 25 2011 *)
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CROSSREFS
| A001157, A064602 A050226, A056650, A064605, A064606, A064607, A064610, A064611, A064612, A048290, A062982, A045345.
Sequence in context: A013002 A012998 A143760 * A132039 A204552 A002668
Adjacent sequences: A064602 A064603 A064604 * A064606 A064607 A064608
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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(15)-a(19) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jun 21 2010
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