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).

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

Author

R. K. Guy, Apr 14 2005

Keywords

• nonn
• easy

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.

Examples

			a(2)=518 because a(1)=412, the distinct prime factors of a(1) are 2 and 103; finally, 1 + 412 + 2 + 103 = 518.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..2000
• Doug Engel, Problem 886, Math. Mag., 48 (1975), 57-58.

Crossrefs

Cf. A003508, A027748, A105210, A105212, A105213.

Programs

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

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]],#Harvey P. Dale, Sep 13 2013 *)

Extensions

More terms from Robert G. Wilson v and Emeric Deutsch, Apr 14 2005