A308560 Numbers divisible by the LCM of all sums of any two digits (at distinct positions).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 102, 110, 120, 140, 150, 204, 210, 220, 240, 252, 280, 306, 330, 360, 408, 420, 440, 480, 510, 540, 550, 630, 660, 770, 840, 880, 990, 1110, 1140, 1212, 1320, 1440, 1512, 2016

Offset

1,2

Comments

The sequence trivially includes the single-digit numbers, their multiples of 10, and more generally any near-repdigit number having all digits equal and nonzero, except for a trailing 0, i.e., of the form d*(10^n-10)/9, 1 <= d <= 9, n > 1.

If a number has more than one digit 0, the relevant LCM is zero and will never divide such a number.

Between 84 and 10^4 there are only 13 terms without digit 0: (252, 1212, 1512, 2112, 2424, 2772, 3636, 4224, 4848, 6216, 6336, 8316, 8448), cf. A308561.

Links

Table of n, a(n) for n=1..66.

Example

For single-digit numbers 1, 2, ..., 9, there is no sum of two digits, and since the LCM of an empty set is taken to be 1, it divides the number.
Two-digit terms are in the sequence iff they are divisible by the sum of their digits. This includes multiples of ten: 10, 20, ..., 90, but also less trivial examples as 12, 18, 21, ...
The first 3-digit term having no digit 0 is 252, divisible by both, 2 + 5 = 7 and  2 + 2 = 4.

Prog

(PARI) is(n, d=digits(n))={n<10||vecsort(d)[2]&&0==n%lcm(concat(vector(-1+n=#d, i, t=d[1+n-i]; vector(n-i, j, t+d[j]))))}

Crossrefs

Cf. A308534, A308561.

Sequence in context: A235697 A085135 A085133 * A285815 A337741 A110806

Adjacent sequences: A308557 A308558 A308559 * A308561 A308562 A308563

Keyword

nonn,base

Author

M. F. Hasler, Jun 07 2019

Status

approved