A334828 Numbers that divide the multiplication of its digits raised to their own powers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 25, 36, 64, 96, 125, 128, 135, 162, 175, 216, 250, 256, 375, 378, 384, 432, 486, 567, 576, 625, 648, 672, 675, 729, 735, 756, 768, 784, 864, 875, 972, 1024, 1176, 1250, 1296, 1372, 1715, 1764, 1944, 2048, 2304, 2500, 2744, 2916, 3087, 3125, 3375, 3456, 3645, 3675, 4096

Offset: 1

Author

Scott R. Shannon, May 13 2020

Keywords

• nonn
• base

Comments

As in A045503 we take 0^0 = 1.

Numbers m that divide A061510(m).

Examples

			5 is a term as 5^5 = 3125 which is divisible by 5.
16 is a term as 1^1*6^6 = 46656 which is divisible by 16.
375 is a term as 3^3*7^7*5^5 = 69486440625 which is divisible by 375.
1176 is a term as 1^1*1^1*7^7*6^6 = 38423222208 which is divisible by 1176.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000312, A045503, A046253, A061510, A243507, A108302.

Programs

Mathematica

pow[n_] := If[n == 0, 1, n^n]; Select[Range[2^12], Divisible[Times @@ (pow /@ IntegerDigits[#]), #] &] (* Amiram Eldar, May 13 2020 *)

PARI

isok(m) = my(d=digits(m)); (prod(k=1, #d, d[k]^d[k]) % m) == 0; \\ Michel Marcus, May 14 2020