A333623 Numbers k such that k is divisible by the sum of digits of all the divisors of k in primorial base (A319715).

1, 2, 3, 4, 14, 22, 40, 64, 90, 104, 120, 160, 169, 175, 182, 220, 272, 275, 338, 360, 500, 550, 640, 646, 752, 775, 792, 858, 928, 930, 1120, 1230, 1280, 1332, 1496, 1710, 2050, 2204, 2303, 2368, 2475, 2584, 2632, 2640, 2806, 2838, 2886, 2898, 3002, 3174, 3192

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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.

Mathematica

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[#]] &]

Crossrefs

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

Sequence in context: A047193 A333622 A019137 * A317737 A188533 A163128

Adjacent sequences: A333620 A333621 A333622 * A333624 A333625 A333626

Keyword

nonn,base

Author

Amiram Eldar, Mar 29 2020

Status

approved