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A105211
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).
6
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
OFFSET
1,1
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.
LINKS
Doug Engel, Problem 886, Math. Mag., 48 (1975), 57-58.
EXAMPLE
a(2)=518 because a(1)=412, the distinct prime factors of a(1) are 2 and 103; finally, 1 + 412 + 2 + 103 = 518.
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]:=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
MATHEMATICA
nxt[n_]:=n+1+Total[Select[Transpose[FactorInteger[n]][[1]], #<n&]]; NestList[ nxt, 412, 50] (* Harvey P. Dale, Sep 13 2013 *)
PROG
(Haskell)
a105211 n = a105211_list !! (n-1)
a105211_list = 412 : map
(\x -> x + 1 + sum (takeWhile (< x) $ a027748_row x)) a105211_list
-- Reinhard Zumkeller, Jan 15 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Apr 14 2005
EXTENSIONS
More terms from Robert G. Wilson v and Emeric Deutsch, Apr 14 2005
STATUS
approved