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

1,2

Comments

As in A045503 we take 0^0 = 1.

Numbers m that divide A061510(m).

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A079041 A133059 A132722 * A048407 A322260 A133504

Adjacent sequences: A334825 A334826 A334827 * A334829 A334830 A334831

Keyword

nonn,base

Author

Scott R. Shannon, May 13 2020

Status

approved