A105210 a(1) = 393; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1). edit.

393, 528, 545, 660, 682, 727, 728, 751, 752, 802, 1206, 1279, 1280, 1288, 1321, 1322, 1986, 2323, 2448, 2471, 2832, 2897, 2898, 2934, 3103, 3240, 3251, 3252, 3529, 3530, 3891, 5192, 5265, 5287, 5616, 5635, 5671, 5832, 5838, 5990, 6597, 7334, 7549, 7550

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.

This suggests that there may be infinitely many different (non-merging) sequences obtained by choosing different starting values.

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)=528 because a(1)=393, the distinct prime factors of a(1) are 3 and 131; finally, 1 + 393 + 3 + 131 = 528.

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]:=393: 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

a[1] = 393; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 44}] (* Robert G. Wilson v, Apr 14 2005 *)
a[1] = 412; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 43}] (* Robert G. Wilson v, Apr 14 2005 *)
a[1] = 668; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 40}] (* Robert G. Wilson v, Apr 14 2005 *)
a[1] = 932; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 40}] (* Robert G. Wilson v, Apr 14 2005 *)
nxt[n_]:=n+1+Total[Select[FactorInteger[n][[All, 1]], #<n&]]; NestList[ nxt, 393, 50] (* Harvey P. Dale, Mar 02 2019 *)

Prog

(Haskell)
a105210 n = a105210_list !! (n-1)
a105210_list = 393 : map
      (\x -> x + 1 + sum (takeWhile (< x) $ a027748_row x)) a105210_list
-- Reinhard Zumkeller, Jan 15 2015

Crossrefs

Cf. A003508, A027748, A105211, A105212, A105213.

Sequence in context: A105233 A048129 A045194 * A256742 A158002 A083752

Adjacent sequences: A105207 A105208 A105209 * A105211 A105212 A105213

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