

A278473


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


0



1, 6, 25, 75, 76, 96, 99, 376, 625, 1376, 1875, 3568, 3751, 4375, 6875, 8001, 8125, 9376, 13568, 28125, 49376, 68751, 89376, 90625, 109375, 109376, 499999, 800001, 890624, 890625, 2890625, 5109376, 5781249, 6640625, 7109376, 8000001, 12109375, 12890625
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..38.
Eric Weisstein's World of Mathematics, Divisor Product
Index entries for sequences related to automorphic numbers
Index entries for sequences related to final digits of numbers


EXAMPLE

6 is in the sequence because 6 has 4 divisors {1,2,3,6} and 1*2*3*6 = 36;
25 is in the sequence because 25 has 3 divisors (1,5,25} and 1*5*25 = 125;
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.


MATHEMATICA

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


CROSSREFS

Cf. A007955, A010051, A011557, A018252, A055642.
Sequence in context: A245679 A211911 A241303 * A281157 A256859 A133714
Adjacent sequences: A278470 A278471 A278472 * A278474 A278475 A278476


KEYWORD

nonn,base


AUTHOR

Ilya Gutkovskiy, Nov 23 2016


STATUS

approved



