This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370675 #30 Mar 06 2024 14:48:04
%S A370675 0,7,156,3399,112025,4505706,213002162
%N A370675 Number of unordered pairs of n-digit numbers k1, k2 such that their product has the same multiset of digits as in both k1 and k2 together.
%C A370675 Since multiplication and multiset union are commutative operations, we count unordered pairs, i.e. we can assume that k1 <= k2.
%C A370675 The sequence is nondecreasing, since for any x,y,p such that x*y=p, x0*y0=p00.
%C A370675 The numbers up to n=7 were verified by at least two independent implementations.
%C A370675 The property of possible residues mod 3 and mod 9 for A370676 also holds for this sequence.
%H A370675 Danila Potapov, <a href="https://habr.com/ru/articles/795935/">Numbers that flip when multiplied</a> (in Russian).
%e A370675 For n=2 the a(2)=7 solutions are:
%e A370675 15 * 93 = 1395
%e A370675 21 * 60 = 1260
%e A370675 21 * 87 = 1827
%e A370675 27 * 81 = 2187
%e A370675 30 * 51 = 1530
%e A370675 35 * 41 = 1435
%e A370675 80 * 86 = 6880
%o A370675 (PARI) a370675(n) = {my (np=0, n1=10^(n-1), n2=10*n1-1); for (k1=n1, n2, my(s1=digits(k1)); for (k2=k1, n2, my (s2=digits(k2)); my(sp=digits(k1*k2)); if (#s1+#s2==#sp && vecsort(concat(s1,s2)) == vecsort(sp), np++))); np} \\ _Hugo Pfoertner_, Feb 26 2024
%Y A370675 Cf. A114258, A370676 (number of such pairs with possibly unequal number of digits).
%Y A370675 Cf. A370678, A370679, A370680.
%K A370675 nonn,base,more
%O A370675 1,2
%A A370675 _Danila Potapov_, Feb 26 2024