This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379834 #21 Jan 11 2025 19:25:27 %S A379834 999,2558,3366,4444,12489,13377,22444,112668,113388,114455,122289, %T A379834 123336,222244,666666,1113399,1113468,1114449,1122455,1133334,1377789, %U A379834 1555888,2222224,2346669,3334689,3344499,4444448,11112778,11114466,11122368,11122449,11222255,11223333,11467779,12366666,13336668 %N A379834 Positive integers with digits in nondescending order whose digit product is an integer power of their digit sum, given power > 1. %C A379834 This sequence would include the terms of A274124 (digit product equal to digit sum) if the power were allowed to be 1. %C A379834 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. %C A379834 Each number of this sequence is an element of a group of permutations of its digits. %C A379834 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. %H A379834 Robert Kinner, <a href="/A379834/a379834.lpr.txt">Pascal Program</a> %e A379834 The product of the digits of 999 equals the sum of the digits, 27, squared. %e A379834 The product of the digits of 666666 equals the cube of the sum of the digits, 36. %o A379834 (Pascal) // See Robert Kinner link. %Y A379834 Cf. A117720, A274124. %K A379834 nonn,base %O A379834 1,1 %A A379834 _Robert Kinner_, Jan 03 2025