OFFSET
1,1
COMMENTS
Numbers k such that A077351(k)=0.
Let s(k) be the sum of the digits of all the divisors of k. The sequence must, of course, include every number k such that 3 divides k but does not divide s(k). Similarly, it must include every k such that 9 divides k but does not divide s(k). The sequence also includes many numbers with relatively few divisors, since the concatenation of their digits offers relatively few opportunities to obtain a multiple of k by permuting them. Of the sequence's 2544 terms below 10000, only four exist that (1) are not primes, (2) are not semiprimes, (3) are not prime powers, (4) are not numbers k that are divisible by 3 but having s(k) not divisible by 3, and (5) are not numbers k that are divisible by 9 but having s(k) not divisible by 9: 242, 2222, 5555, and 7777.
LINKS
Jon E. Schoenfield, Table of n, a(n) for n=1..2544
EXAMPLE
The divisors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108, and concatenating all their digits gives the 19-digit number 1234691218273654108; no permutation of those 19 digits yields a result that is divisible by 108, so 108 is in the sequence.
The divisors of 14 are 1, 2, 7, and 14, and concatenating all their digits gives the 5-digit number 12714; those 5 digits can be permuted to yield a result (e.g., 21714) that is divisible by 14, so 14 is not in the sequence.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Jon E. Schoenfield, Jul 02 2010
STATUS
approved