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 A070982 Smallest integer k such that n divides sigma(k). 10
 1, 3, 2, 3, 8, 5, 4, 7, 10, 19, 43, 6, 9, 12, 8, 21, 67, 10, 37, 19, 20, 43, 137, 14, 149, 45, 34, 12, 173, 24, 16, 21, 86, 67, 76, 22, 73, 37, 18, 27, 163, 20, 257, 43, 40, 137, 281, 33, 52, 149, 101, 63, 211, 34, 109, 28, 49, 173, 353, 24, 169, 48, 32, 93, 72, 86, 401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 József Sándor, The sum-of-divisors minimum and maximum functions, Research Report Collection, Volume 8, Issue 1, 2005. See p. 3. FORMULA a(n) = min( k : sigma(k) == 0 mod(n) ). Sum(k=1, n, a(k)) seems to be asymptotic to c*n^2 with probably 1.1 < c < 1.2. By Xylouris' form of Linnk's theorem, a(n) << n^5. Can this be improved? - Charles R Greathouse IV, Mar 09 2017 MATHEMATICA a = ConstantArray[1, 67]; k = 1; While[Length[vac = Rest[Flatten[Position[a, 1]]]] > 0, k++; a[[Intersection[Divisors[DivisorSigma[1, k]], vac]]] *= k]; a (* Ivan Neretin, May 15 2015 *) With[{dsk=Table[{k, DivisorSigma[1, k]}, {k, 500}]}, Table[SelectFirst[ dsk, Divisible[#[[2]], n]&], {n, 70}]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 04 2018 *) PROG (PARI) a(n)=my(s); while(sigma(s++)%n, ); s CROSSREFS Right diagonal of A074625. Cf. A005179 (analog for number of divisors), A061026 (analog for Euler totient). Sequence in context: A227470 A218396 A331926 * A275520 A187153 A213265 Adjacent sequences:  A070979 A070980 A070981 * A070983 A070984 A070985 KEYWORD nonn,look AUTHOR Benoit Cloitre, May 24 2002 STATUS approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)