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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). 6
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 (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

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

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]], #<n&]]; NestList[nx, 932, 40] (* Harvey P. Dale, Jul 24 2011 *)

PROG

(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

CROSSREFS

Cf. A027748, A003508, A105210, A105211, A105212.

Sequence in context: A035856 A093231 A252530 * A347852 A171348 A232380

Adjacent sequences:  A105210 A105211 A105212 * A105214 A105215 A105216

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

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Last modified May 21 06:36 EDT 2022. Contains 353889 sequences. (Running on oeis4.)