

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
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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

Jud McCranie


EXTENSIONS

Edited by M. F. Hasler, Nov 22 2019


STATUS

approved



