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A343925 Irregular triangle read by rows: n-th row gives the numbers > 1 that can be multiplied by n the maximum number of times, see A343924, such that each product has distinct digits.

%I A343925 #24 Feb 19 2025 16:12:54
%S A343925 2,2,2,2,2,2,5,2,3,2,13,14,15,18,35,72,77,2,2,5,2,2,2,3,6,17,3,13,2,2,
%T A343925 7,12,2,2,5,39,3,2,7,17,78,3,2,2,4,2,5,9,12,18,93,3,17,5,3,2,4,2,5,2,
%U A343925 2,2,9,2,3,5,6,7,11,12,15,21,24,25,34,59,74,87,107,113,118,127,158,173,207
%N A343925 Irregular triangle read by rows: n-th row gives the numbers > 1 that can be multiplied by n the maximum number of times, see A343924, such that each product has distinct digits.
%C A343925 See A343924 for the maximum number of times the numbers in each row can multiply n to produce a series of products with distinct digits.
%C A343925 The number of terms in each row is extremely variable. For n below 1000 the numbers 556, 748, 813, 818, 848 can only be multiplied one time before a product with non-distinct digits is produced. For 556, for example, there are 7002 different numbers which satisfy this condition, the list starting with 5, 7, 15, 17, 19, ... . In comparison the next row for 557 has one term, 25, which can be multiplied by 557 the maximum of three times.
%C A343925 All rows correspond to numbers ending in two or more zeros, for example 100, have no terms as any product will also end in at least that many zeros.
%H A343925 Scott R. Shannon, <a href="/A343925/a343925.txt">Table for n = 1..1000</a>.
%F A343925 row(n) has no terms for n > 4938271605 or for any number n ending in two or more 0's.
%e A343925 row(1) = 2 as 1 can be multiplied by 2 the maximum of 15 times producing products with distinct digits. The products are: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16348, 32768.
%e A343925 row(11) = 13, 14, 15, 18, 35, 72, 77 as these numbers can be multiplied by 11 the maximum of 3 times producing products with distinct digits. For example choosing 13 the products are 143, 1859, 24167.
%e A343925 The table begins:
%e A343925 .
%e A343925 2;
%e A343925 2;
%e A343925 2;
%e A343925 2;
%e A343925 2;
%e A343925 2;
%e A343925 5;
%e A343925 2;
%e A343925 3;
%e A343925 2;
%e A343925 13, 14, 15, 18, 35, 72, 77;
%e A343925 2;
%e A343925 2;
%e A343925 5;
%e A343925 2;
%e A343925 2;
%e A343925 2, 3, 6, 17;
%e A343925 3, 13;
%e A343925 ...
%Y A343925 Cf. A343924, A343921 (addition), A010784, A003991, A043537.
%K A343925 nonn,base,tabf
%O A343925 1,1
%A A343925 _Scott R. Shannon_, May 04 2021