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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. 2
3, 7, 9, 11, 12, 13, 17, 18, 19, 21, 22, 23, 27, 29, 31, 33, 36, 37, 39, 41, 43, 45, 47, 48, 49, 53, 54, 55, 57, 59, 61, 63, 67, 71, 72, 73, 74, 75, 77, 79, 81, 83, 84, 89, 91, 93, 97, 99, 101, 103, 107, 108, 109, 111, 113, 117, 121, 126, 129, 131, 135, 137, 139, 143, 144 (list; graph; refs; listen; history; text; internal format)
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

Cf. A077351.

Sequence in context: A333911 A276492 A023992 * A097270 A109802 A180442

Adjacent sequences:  A179194 A179195 A179196 * A179198 A179199 A179200

KEYWORD

base,nonn

AUTHOR

Jon E. Schoenfield, Jul 02 2010

STATUS

approved

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Last modified June 15 11:17 EDT 2021. Contains 345048 sequences. (Running on oeis4.)