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Search: id:A105211
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| A105211 |
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a(1) = 412; 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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2
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| 412, 518, 565, 684, 709, 710, 789, 1056, 1073, 1140, 1170, 1194, 1399, 1400, 1415, 1704, 1781, 1932, 1968, 2015, 2065, 2137, 2138, 3210, 3328, 3344, 3377, 3696, 3720, 3762, 3798, 4015, 4105, 4932, 5075, 5117, 5185, 5269, 5760, 5771, 6000, 6011, 6012
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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Problem 886, Math. Mag., 48 (1975), 57-58.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..2000
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EXAMPLE
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a(2)=518 because a(1)=412, the distinct prime factors of a(1) are 2 and 103; finally, 1+412+2+103=518.
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MAPLE
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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]:=412: for n from 2 to 50 do a[n]:=1+a[n-1]+p(a[n-1]) od:seq(a[n], n=1..50); (Deutsch)
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CROSSREFS
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Sequence in context: A146075 A090123 A055018 this_sequence A081378 A027661 A096032
Adjacent sequences: A105208 A105209 A105210 this_sequence A105212 A105213 A105214
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KEYWORD
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nonn,easy
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AUTHOR
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R. K. Guy, Apr 14, 2005
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EXTENSIONS
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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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