A105213 a(1) = 932; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).

932, 1168, 1244, 1558, 1621, 1622, 2436, 2478, 2550, 2578, 3870, 3924, 4039, 4624, 4644, 4693, 4726, 4885, 5868, 6037, 6038, 9060, 9222, 9310, 9344, 9420, 9588, 9658, 10111, 10112, 10194, 11899, 12136, 12217, 12880, 12918, 15077, 15078, 15450

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)=1168 because a(1)=932, the distinct prime factors of a(1) are 2 and 233; finally, 1 + 932 + 2 + 233 = 1168.
		

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. A027748, A003508, A105210, A105211, A105212.

Programs

Haskell

a105213 n = a105213_list !! (n-1)
a105213_list = 932 : map
      (\x -> x + 1 + sum (takeWhile (< x) $ a027748_row x)) a105213_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]:=932: for n from 2 to 46 do a[n]:=1+a[n-1]+p(a[n-1]) od:seq(a[n],n=1..46); # Emeric Deutsch, Apr 14 2005

Mathematica

nx[n_]:=n+1+Total[Select[Transpose[FactorInteger[n]][[1]],#Harvey P. Dale, Jul 24 2011 *)

Extensions

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