A333623 - OEIS

A333623

Numbers k such that k is divisible by the sum of digits of all the divisors of k in primorial base (A319715).

%I #10 Oct 12 2023 06:20:09

%S 1,2,3,4,14,22,40,64,90,104,120,160,169,175,182,220,272,275,338,360,

%T 500,550,640,646,752,775,792,858,928,930,1120,1230,1280,1332,1496,

%U 1710,2050,2204,2303,2368,2475,2584,2632,2640,2806,2838,2886,2898,3002,3174,3192

%N Numbers k such that k is divisible by the sum of digits of all the divisors of k in primorial base (A319715).

%H Amiram Eldar, <a href="/A333623/b333623.txt">Table of n, a(n) for n = 1..10000</a>

%F 14 is a term since its divisors are {1, 2, 7, 14}, their representations in primorial base (A049345) are {1, 10, 101, 210}, and their sum of sums of digits is 1 + (1 + 0) + (1 + 0 + 1) + (2 + 1 + 0) = 7 which is a divisor of 14.

%t max = 5; bases = Prime@Range[max, 1, -1]; nmax = Times @@ bases - 1; primDigSum[n_] := Plus @@ IntegerDigits[n, MixedRadix[bases]]; primDivDigDum[n_] := DivisorSum[n, primDigSum[#] &]; Select[Range[nmax], Divisible[#, primDivDigDum[#]] &]

%Y Cf. A049345, A093705, A276150, A319715, A333617, A333619, A333620, A333622.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Mar 29 2020