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 A105210 a(1) = 393; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1). 6
 393, 528, 545, 660, 682, 727, 728, 751, 752, 802, 1206, 1279, 1280, 1288, 1321, 1322, 1986, 2323, 2448, 2471, 2832, 2897, 2898, 2934, 3103, 3240, 3251, 3252, 3529, 3530, 3891, 5192, 5265, 5287, 5616, 5635, 5671, 5832, 5838, 5990, 6597, 7334, 7549, 7550 (list; graph; refs; listen; history; text; internal format)
 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. This suggests that there may be infinitely many different (non-merging) sequences obtained by choosing different starting values. REFERENCES Problem 886, Math. Mag., 48 (1975), 57-58. LINKS T. D. Noe, Table of n, a(n) for n=1..2000 EXAMPLE a(2)=528 because a(1)=393, the distinct prime factors of a(1) are 3 and 131; finally, 1+393+3+131=528. 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]:=393: 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) MATHEMATICA a[1] = 393; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 44}] (from Robert G. Wilson v, Apr 14 2005) a[1] = 412; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 43}] (from Robert G. Wilson v, Apr 14 2005) a[1] = 668; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 40}] (from Robert G. Wilson v, Apr 14 2005) a[1] = 932; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 40}] (from Robert G. Wilson v, Apr 14 2005) CROSSREFS Sequence in context: A105233 A048129 A045194 * A158002 A083752 A047825 Adjacent sequences:  A105207 A105208 A105209 * A105211 A105212 A105213 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

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