A278473 Numbers n such that product of divisors of n ends with n and n is nonprime (A018252).

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

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: A211911 A339194 A241303 * A281157 A346975 A354396

Adjacent sequences: A278470 A278471 A278472 * A278474 A278475 A278476

Keyword

nonn,base

Author

Ilya Gutkovskiy, Nov 23 2016

Status

approved