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a(n) = the smallest multiple of n with n digits and exactly n divisors. a(n) = 0 if no such number exists.
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%I #32 Jun 02 2024 20:10:52

%S 1,0,0,0,0,0,0,10000024,100580841,0,25937424601,100000000068,0,0,0,

%T 1000000000001152,0,100000000000000404,0,10000000000000000880,0,0,0,

%U 100000000000000000001184,1000060001350013500050625,0,100000000015460000000597529,1000000000000000000000022464

%N a(n) = the smallest multiple of n with n digits and exactly n divisors. a(n) = 0 if no such number exists.

%C Conjecture: a(n) > 0 for all nonsquarefree n except for n = 4. - _Jon E. Schoenfield_, Jun 01 2024

%H Jon E. Schoenfield, <a href="/A182749/b182749.txt">Table of n, a(n) for n = 1..100</a>

%F A000005(a(n)) = n for a(n) > 0.

%F a(n) <= A182750(n).

%Y Cf. A000005, A073904, A182750.

%K nonn,base

%O 1,8

%A _Jaroslav Krizek_, Nov 27 2010

%E a(16), a(18), a(20) corrected by _Jon E. Schoenfield_, May 26 2024

%E a(21)-a(23) (implied by A182750) from _Pontus von Brömssen_, May 26 2024

%E a(24)-a(25) from _Michael S. Branicky_, May 26 2024

%E a(26)-a(28) from _Jon E. Schoenfield_, May 26 2024