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A043306
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Sum of all digits in all base b representations for n, for 2<=b<=n.
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2
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1, 3, 4, 8, 10, 16, 17, 21, 25, 35, 34, 46, 52, 60, 58, 74, 73, 91, 92, 104, 114, 136, 128, 144, 156, 168, 171, 199, 193, 223, 221, 241, 257, 281, 261, 297, 315, 339, 333, 373, 367, 409, 416, 430, 452, 498, 472, 508
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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REFERENCES
| J.-C. Puchta, J. Spilker, Altes und Neues zur Quersumme, Math. Semesterber., 49 (2002), 209-226.
V. Shevelev, Compact integers and factorials, Acta Arith. 126 (2007), no.3, 195-236 (cf. p.205).
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FORMULA
| a(n)=(n-1)*n-sum(i=2..n, (i-1)*sum(r>=1, floor(n/i^r) ) );
a(n)<=(n-1)^2*log(n+1)/log(n). Problem: find a better upper estimate. -Vladimir Shevelev(shevelev(AT)bgu.ac.il), Jun 03 2011
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EXAMPLE
| 5=101_2=12_3=11_4=10_5. Thus a(5)=2+3+2+1=8.
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MATHEMATICA
| Table[Sum[Total[First[RealDigits[n, i]]], {i, 2, n}], {n, 2, 80}] (* Carl Najafi, Aug 16 2011 *)
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CROSSREFS
| Cf. A043000, A068953, A191251, A191322, A191350
Sequence in context: A080085 A063414 A026494 * A131355 A092534 A005232
Adjacent sequences: A043303 A043304 A043305 * A043307 A043308 A043309
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KEYWORD
| nonn,base
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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