A278474 Numbers n such that the product of proper divisors of n ends with n and n is not a multiplicatively perfect number (A007422).

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

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: A179152 A193069 A347422 * A327946 A288949 A108190

Adjacent sequences: A278471 A278472 A278473 * A278475 A278476 A278477

Keyword

nonn,base

Author

Ilya Gutkovskiy, Nov 23 2016

Status

approved