cp's OEIS Frontend

A179197 Numbers k such that there exists no multiple of k whose digits are a permutation of all the digits of all the divisors of k.

%I A179197 #3 Aug 31 2013 19:33:55
%S A179197 3,7,9,11,12,13,17,18,19,21,22,23,27,29,31,33,36,37,39,41,43,45,47,48,
%T A179197 49,53,54,55,57,59,61,63,67,71,72,73,74,75,77,79,81,83,84,89,91,93,97,
%U A179197 99,101,103,107,108,109,111,113,117,121,126,129,131,135,137,139,143,144
%N A179197 Numbers k such that there exists no multiple of k whose digits are a permutation of all the digits of all the divisors of k.
%C A179197 Numbers k such that A077351(k)=0.
%C A179197 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.
%H A179197 Jon E. Schoenfield, <a href="/A179197/b179197.txt">Table of n, a(n) for n=1..2544</a>
%e A179197 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.
%e A179197 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.
%Y A179197 Cf. A077351.
%K A179197 base,nonn
%O A179197 1,1
%A A179197 _Jon E. Schoenfield_, Jul 02 2010