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Search: id:A105212
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| A105212 |
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a(1) = 668; 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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| 668, 838, 1260, 1278, 1355, 1632, 1655, 1992, 2081, 2082, 2435, 2928, 2995, 3600, 3611, 3792, 3877, 3878, 4165, 4195, 5040, 5058, 5345, 6420, 6538, 7015, 7105, 7147, 8176, 8259, 11016, 11039, 11149, 11150, 11381, 12000, 12011, 12012, 12049, 12050
(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)=838 because a(1)=668, the distinct prime factors of a(1) are 2 and 167; finally, 1+668+2+167=838.
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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]:=668: 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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CROSSREFS
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Sequence in context: A046694 A138563 A092797 this_sequence A067875 A053085 A057695
Adjacent sequences: A105209 A105210 A105211 this_sequence A105213 A105214 A105215
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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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