

A278474


Numbers n such that the product of proper divisors of n ends with n and n is not a multiplicatively perfect number (A007422).


0



24, 36, 76, 375, 376, 432, 624, 625, 693, 875, 999, 2499, 4557, 8307, 9375, 9376, 9999, 34375, 40625, 47943, 50001, 59375, 81249, 90624, 90625, 99999, 109376, 186432, 218751, 586432, 609375, 690624, 718751, 781249, 890625, 954193, 968751, 999999, 2109375, 2890624, 2890625
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OFFSET

1,1


COMMENTS

Numbers n such that A007956(n) == n (mod A011557(A055642(n))) and A000005(n) <> 4.


LINKS

Table of n, a(n) for n=1..41.
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

24 is in the sequence because 24 has 7 proper divisors {1,2,3,4,6,8,12} and 1*2*3*4*6*8*12 = 13824;
36 is in the sequence because 36 has 8 proper divisors {1,2,3,4,6,9,12,18} and 1*2*3*4*6*9*12*18 = 279936;
76 is in the sequence because 76 has 5 proper divisors {1,2,4,19,38} and 1*2*4*19*38 = 5776, etc.


MATHEMATICA

Select[Range[3000000], Mod[Sqrt[#1]^DivisorSigma[0, #1]/#1, 10^IntegerLength[#1]] == #1 && Sqrt[#1]^DivisorSigma[0, #1] != #1^2 & ]


CROSSREFS

Cf. A000005, A007422, A007956, A011557, A055642, A210994
Sequence in context: A261022 A179152 A193069 * A288949 A108190 A185489
Adjacent sequences: A278471 A278472 A278473 * A278475 A278476 A278477


KEYWORD

nonn,base


AUTHOR

Ilya Gutkovskiy, Nov 23 2016


STATUS

approved



