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 A094339 Beginning with 2, least number not occurring earlier that divides the sum of all previous terms. 5
 2, 1, 3, 6, 4, 8, 12, 9, 5, 10, 15, 25, 20, 24, 16, 32, 48, 30, 18, 36, 27, 13, 7, 53, 106, 265, 159, 318, 212, 14, 107, 321, 214, 428, 642, 535, 35, 21, 181, 11, 33, 22, 23, 59, 70, 28, 151, 29, 19, 233, 466, 2563, 699, 932, 40, 26, 38, 31, 61, 39, 49, 98, 42, 56, 50, 197, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: this is a rearrangement of natural numbers. Comments from Zak Seidov, Feb 19 2005: "Changing the seed produces different sequences, some of which merge into each other: s2=2,1,3,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53 s3=3,1,2,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53 s4=4,1,5,2,3,15,6,9,45,10,20,8,16,12,13,169,26,7,53,106,265,159,18 s5=5,1,2,4,3,15,6,9,45,10,20,8,16,12,13,169,26,7,53,106,265,159,18 s6=6,1,7,2,4,5,25,10,3,9,8,16,12,18,14,20,32,24,27,81,36,15,75,30,40 s7=7,1,2,5,3,6,4,14,21,9,8,10,15,35,20,16,11,17,12,18,13,19,38,76,95 s8=8,1,3,2,7,21,6,4,13,5,10,16,12,9,39,26,14,28,32,64,20,17,51,24,18 s9=9,1,2,3,5,4,6,10,8,12,15,25,20,24,16,32,48,30,18,36,27,13,7,53,106 s10=10,1,11,2,3,9,4,5,15,6,22,8,12,18,7,19,38,95,57,114,24,16,31,17,32 s11=11,1,2,7,3,4,14,6,8,28,12,16,56,21,9,18,24,5,35,10,29,319,22,15,25,20,30 In every case one may ask if the result is a rearrangement of the natural numbers." LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 EXAMPLE The sum of first 7 terms is 36, hence a(8) = 9 is the least divisor of 36 not occurring earlier. MAPLE A094339 := proc(nmax) local a, n, sprev, i; a := [2] ; while nops(a) < nmax do sprev := add(i, i=a) ; n := 1 ; while sprev mod n <> 0 or n in a do n := n+1 ; od ; a := [op(a), n] ; od ; RETURN(a) ; end: A094339(100) ; # R. J. Mathar, Apr 30 2007 MATHEMATICA a={2}; Do[AppendTo[a, Min[Select[Divisors[Plus@@a], !MemberQ[a, #]&]]], {t, 2, 70}]; a (* Ivan Neretin, Apr 13 2015 *) PROG (PARI) v=[2]; n=1; while(#v<100, if(!vecsearch(vecsort(v, , 8), n)&&!(vecsum(v)%n), v=concat(v, n); n=0); n++); v \\ Derek Orr, Apr 13 2015 CROSSREFS Cf. A094340, A094341. Sequence in context: A209160 A257881 A268182 * A317788 A120576 A063707 Adjacent sequences:  A094336 A094337 A094338 * A094340 A094341 A094342 KEYWORD nonn AUTHOR Amarnath Murthy, May 17 2004 EXTENSIONS Corrected and extended by R. J. Mathar, Apr 30 2007 STATUS approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)