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A105213
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a(1) = 932; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
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6
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932, 1168, 1244, 1558, 1621, 1622, 2436, 2478, 2550, 2578, 3870, 3924, 4039, 4624, 4644, 4693, 4726, 4885, 5868, 6037, 6038, 9060, 9222, 9310, 9344, 9420, 9588, 9658, 10111, 10112, 10194, 11899, 12136, 12217, 12880, 12918, 15077, 15078, 15450
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| In Math. Mag. 48 (1975) 301 one finds "C. W. Trigg, C. C. Oursler and R. Cormier and J. L. Selfridge have sent calculations on Problem 886 [Nov 1973] for which we had received only partial results [Jan 1975]. Cormier and Selfridge sent the following results: There appear to be five sequences beginning with integers less than 1000 which do not merge. These sequences were carried out to 10^8 or more." The five sequences are A003508, A105210-A105213.
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REFERENCES
| Problem 886, Math. Mag., 48 (1975), 57-58.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..2000
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EXAMPLE
| a(2)=1168 because a(1)=932, the distinct prime factors of a(1) are 2 and 233; finally, 1+932+2+233=1168.
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MAPLE
| with(numtheory): p:=proc(n) local nn, ct, s: if isprime(n)=true then s:=0 else nn:=convert(factorset(n), list): ct:=nops(nn): s:=sum(nn[j], j=1..ct):fi: end: a[1]:=932: for n from 2 to 46 do a[n]:=1+a[n-1]+p(a[n-1]) od:seq(a[n], n=1..46); (Deutsch)
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MATHEMATICA
| nx[n_]:=n+1+Total[Select[Transpose[FactorInteger[n]][[1]], #<n&]]; NestList[nx, 932, 40] (* From Harvey P. Dale, Jul 24 2011 *)
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CROSSREFS
| Sequence in context: A158679 A035856 A093231 * A171348 A029570 A120810
Adjacent sequences: A105210 A105211 A105212 * A105214 A105215 A105216
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KEYWORD
| nonn,easy
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AUTHOR
| R. K. Guy, Apr 14, 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 14 2005
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