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

Author

Ilya Gutkovskiy, Nov 23 2016

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• 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

Crossrefs

Cf. A000005, A007422, A007956, A011557, A055642, A210994

Programs

Mathematica

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