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

1,1

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

T. D. Noe, Table of n, a(n) for n = 1..2000

Doug Engel, Problem 886, Math. Mag., 48 (1975), 57-58.

Example

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

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

Prog

(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

Crossrefs

Cf. A003508, A027748, A105210, A105211, A105213.

Sequence in context: A138563 A327908 A092797 * A067875 A224558 A250670

Adjacent sequences: A105209 A105210 A105211 * A105213 A105214 A105215

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