|
|
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).
|
|
6
|
|
|
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
(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.
|
|
LINKS
|
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|