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Number of times the digits are repeated in A045869.
0

%I #12 Nov 13 2022 02:06:32

%S 1,1,2,1,1,2,2,4,2,2,2,1,6,4,4,8,8,8,4,3,6,3,12,3,3,6,6,12,12,6,6,10,

%T 10,10,5,10,5,5,20,5,10,7,14,28,22,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%U 2,2,2,2,2,2,2,2,2,2,2,4,22,2,2,2,4,2,2,2,2,2,2,2,2,2,2,2,2,2,4,2,4,2,2

%N Number of times the digits are repeated in A045869.

%H Naohiro Nomoto, <a href="https://web.archive.org/web/20000916012426/http://www.geocities.co.jp/Technopolis/1793/09digit.htm">In the list of divisors of n, ...</a>

%e A045869(1) = 2034, and the divisors of 2034_5 = 269 (a prime) are 1 and 269; in base 5, these are 1 and 2034. Each digit from 0 through 4 appears exactly once, so a(1) = 1.

%e A045869(2) = 2403; 2403_5 = 353 (a prime) has divisors 1 and 353, which in base 5 are 1 and 2403, so each digit in 0..4 appears exactly once, so a(2) = 2.

%e A045869(3) = 2430; 2430_5 = 365 = 5*73, so its divisors are 1, 5, 73, and 365, which in base 5 are 1, 10, 243, and 2430, so each digit in 0..4 appears exactly twice, so a(3) = 2.

%Y Cf. A038564, A038565, A045869.

%K easy,nonn,base

%O 0,3

%A _Naohiro Nomoto_

%E Examples edited by _Jon E. Schoenfield_, Nov 12 2022