A278473 - OEIS

%I #7 Nov 27 2016 21:45:35

%S 1,6,25,75,76,96,99,376,625,1376,1875,3568,3751,4375,6875,8001,8125,

%T 9376,13568,28125,49376,68751,89376,90625,109375,109376,499999,800001,

%U 890624,890625,2890625,5109376,5781249,6640625,7109376,8000001,12109375,12890625

%N Numbers n such that product of divisors of n ends with n and n is nonprime (A018252).

%C Numbers n such that A007955(n) == n (mod A011557(A055642(n))) and A010051(n) = 0.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorProduct.html">Divisor Product</a>

%H <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%e 6 is in the sequence because 6 has 4 divisors {1,2,3,6} and 1*2*3*6 = 36;

%e 25 is in the sequence because 25 has 3 divisors (1,5,25} and 1*5*25 = 125;

%e 75 is in the sequence because 75 has 6 divisors {1,3,5,15,25,75} and 1*3*5*15*25*75 = 421875, etc.

%t Select[Range[15000000], Mod[Sqrt[#1]^DivisorSigma[0, #1], 10^IntegerLength[#1]] == #1 &&  !PrimeQ[#1] & ]

%Y Cf. A007955, A010051, A011557, A018252, A055642.

%K nonn,base

%O 1,2

%A _Ilya Gutkovskiy_, Nov 23 2016