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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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6
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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
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OFFSET
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1,1
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COMMENTS
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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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LINKS
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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); # Emeric Deutsch, Apr 14 2005
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MATHEMATICA
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nxt[n_]:=n+1+Total[Select[Transpose[FactorInteger[n]][[1]], #<n&]]; NestList[ nxt, 412, 50] (* Harvey P. Dale, Sep 13 2013 *)
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PROG
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(Haskell)
a105211 n = a105211_list !! (n-1)
a105211_list = 412 : map
(\x -> x + 1 + sum (takeWhile (< x) $ a027748_row x)) a105211_list
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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