A105212 a(1) = 668; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).

668, 838, 1260, 1278, 1355, 1632, 1655, 1992, 2081, 2082, 2435, 2928, 2995, 3600, 3611, 3792, 3877, 3878, 4165, 4195, 5040, 5058, 5345, 6420, 6538, 7015, 7105, 7147, 8176, 8259, 11016, 11039, 11149, 11150, 11381, 12000, 12011, 12012, 12049, 12050

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)=838 because a(1)=668, the distinct prime factors of a(1) are 2 and 167; finally, 1 + 668 + 2 + 167 = 838.
		

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, A105211, A105213.

Programs

Haskell

a105212 n = a105212_list !! (n-1)
a105212_list = 668 : map
      (\x -> x + 1 + sum (takeWhile (< x) $ a027748_row x)) a105212_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]:=668: 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

Extensions

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