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Smallest integer with A002191(n) divisors, i.e., the number of divisors equals the sum of the divisors of a different number.
0

%I #10 Jan 19 2023 22:35:22

%S 1,4,6,12,64,24,60,4096,192,144,180,240,360,960,720,1073741824,840,

%T 1260,786432,36864,1680,2880,15360,2520,6300,6720,2359296,5040,

%U 3221225472,14400,983040,10080,206158430208,184320,15120,20160,25200

%N Smallest integer with A002191(n) divisors, i.e., the number of divisors equals the sum of the divisors of a different number.

%F A000005(a(n)) = A002191(n). I.e., if function A000005 is applied to this sequence, then values of A002191 are obtained. These terms are taken from A005179.

%F a(n) = A005179(A002191(n)). - _David Wasserman_, Jun 06 2002

%e For all values of sigma(x), i.e., of A002191, the smallest number with identical number of divisors is found at A005179(sigma(x)). E.g., 8 = A002191(6) is a possible divisor sum. The smallest number which has 8 divisors is 24 = A005179(8). See also comment to A008864, with special solutions of equation: sigma(x) = tau(y) = A000203(x) = A000005(y).

%Y Cf. A000005, A000203, A002191, A005179, A008864.

%K nonn

%O 1,2

%A _Labos Elemer_, May 28 2001

%E More terms from _David Wasserman_, Jun 06 2002

%E Offset corrected by _Sean A. Irvine_, Jan 19 2023