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 A051444 Smallest k such that sigma(k) = n, or 0 if there is no such k, where sigma = A000203 = sum of divisors. 18
 1, 0, 2, 3, 0, 5, 4, 7, 0, 0, 0, 6, 9, 13, 8, 0, 0, 10, 0, 19, 0, 0, 0, 14, 0, 0, 0, 12, 0, 29, 16, 21, 0, 0, 0, 22, 0, 37, 18, 27, 0, 20, 0, 43, 0, 0, 0, 33, 0, 0, 0, 0, 0, 34, 0, 28, 49, 0, 0, 24, 0, 61, 32, 0, 0, 0, 0, 67, 0, 0, 0, 30, 0, 73, 0, 0, 0, 45, 0, 57, 0, 0, 0, 44, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Column 1 of A299762. - Omar E. Pol, Mar 14 2018 This is a right inverse of sigma = A000203 on A002191 = range(sigma): if n is in A002191, then there is some x with sigma(x) = n, and by definition a(n) is the smallest such x, so sigma(a(n)) = n. - M. F. Hasler, Nov 22 2019 REFERENCES R. K. Guy, Unsolved Problems Theory of Numbers, B1. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: invphi.gp, Oct. 2005 EXAMPLE sigma(1) = 1, so a(1) = 1. There is no k with sigma(k) = 2, since sigma(k) >= k + 1 for all k > 1 and sigma(1) = 1, so a(2) = 0. sigma(4) = 7, and 4 is the smallest (since only) such number, so a(7) = 4. 6 and 12 are the only k with sigma(k) = 12, so 6 is the smallest and a(12) = 6. MATHEMATICA Do[ k = 1; While[ DivisorSigma[ 1, k ] != n && k < 10^4, k++ ]; If[ k != 10^4, Print[ k ], Print[ 0 ] ], {n, 1, 100} ] PROG (PARI) a(n)=for(k=1, n, if(sigma(k)==n, return(k))); 0 \\ Charles R Greathouse IV, Mar 09 2014 (PARI) A051444(n)=if(n=invsigma(n), vecmin(n)) \\ See Alekseyev link for invsigma(). An update including invsigmaMin = A051444 is planned. - M. F. Hasler, Nov 21 2019 CROSSREFS Cf. A000203, A002192, A007626, A007369 (positions of zeros), A299762. Sequence in context: A277516 A322333 A240667 * A299762 A057637 A258913 Adjacent sequences:  A051441 A051442 A051443 * A051445 A051446 A051447 KEYWORD nonn,nice AUTHOR EXTENSIONS Edited by M. F. Hasler, Nov 22 2019 STATUS approved

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Last modified April 8 08:04 EDT 2020. Contains 333313 sequences. (Running on oeis4.)