A379834 Positive integers with digits in nondescending order whose digit product is an integer power of their digit sum, given power > 1.

999, 2558, 3366, 4444, 12489, 13377, 22444, 112668, 113388, 114455, 122289, 123336, 222244, 666666, 1113399, 1113468, 1114449, 1122455, 1133334, 1377789, 1555888, 2222224, 2346669, 3334689, 3344499, 4444448, 11112778, 11114466, 11122368, 11122449, 11222255, 11223333, 11467779, 12366666, 13336668

Offset: 1

Author

Robert Kinner, Jan 03 2025

Keywords

• nonn
• base

Comments

This sequence would include the terms of A274124 (digit product equal to digit sum) if the power were allowed to be 1.

This sequence is similar to A117720 (digit product is the square of the digit sum) except that powers > 2 are also included, and that A117720 does not require nondescending digits. These results are from empirical observation.

Each number of this sequence is an element of a group of permutations of its digits.

Since both addition and multiplication are commutative, it is only necessary to select one representative member of each digit permutation group. The member with digits in nondescending order is chosen.

Examples

			The product of the digits of 999 equals the sum of the digits, 27, squared.
The product of the digits of 666666 equals the cube of the sum of the digits, 36.
		

Links

• Robert Kinner, Pascal Program

Crossrefs

Cf. A117720, A274124.

Programs

Pascal

// See Robert Kinner link.