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A175350
a(n) = the smallest positive integer not yet occurring such that the number of divisors of Sum_{k=1..n} a(k) is exactly n.
4
1, 2, 6, 5, 67, 11, 637, 12, 348, 47, 57913, 26, 472366, 463, 26105, 15, 42488697, 118, 344373650, 136, 2089071, 2496, 30991547417, 7, 332851440, 93936, 3467844, 590, 22845074981535, 31, 183014339639657, 13, 13947373787
OFFSET
1,2
COMMENTS
It seems likely that this is a permutation of the positive integers. Is it?
FORMULA
Sum_{k=1..n} a(k) = A175351(n).
EXAMPLE
a(4) = k where sigma(a(1) + a(2) + a(3) + k) = sigma(9 + k) = 4. The next number larger than 9 having four divisors is 10. This would give k = 1, which is in the sequence. The next number larger than 10 having four divisors is 14. This would give k = 14 - 9 = 5, which isn't already in the sequence. Therefore, a(4) = 5. - David A. Corneth, Mar 08 2017
MATHEMATICA
a[1]=1; a[n_]:=a[n]=Module[{an=First[Complement[Range[n], a/@Range[n-1]]]},
While[DivisorSigma[0, Sum[a[i], {i, n-1}]+an]!=n||MemberQ[a/@Range[n-1], an], an++];
an]; a/@Range[16] (* Ivan N. Ianakiev, Mar 08 2017 *)
CROSSREFS
Sequence in context: A283475 A343995 A358746 * A085057 A069113 A298329
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 19 2010
EXTENSIONS
More terms from Farideh Firoozbakht, Mar 20 2010
STATUS
approved