A262092 - OEIS

%I #27 Dec 31 2021 12:17:53

%S 244,1459,6514,76438,157596,313625,6586433,9057586,1043820406,

%T 756738746,344050075,11346057072,37878721692554416,375609204308055082,

%U 40091536165423401387,244405038116365070846858,183144838903847612823687,2307549584666787613389634

%N Amicable digital pairs: The larger number of a pair (x,y) with x <> y such that, in decimal notation and with an appropriate number of leading zeros prepended, x=(x_m...x_1x_0)_{10}, y=(y_m...y_1y_0)_{10}, x = y_m^m + ... + y_1^m + y_0^m, and y = x_m^m + ... + x_1^m + x_0^m.

%H D. Knuth, <a href="http://www-cs-faculty.stanford.edu/~knuth/amicable_digit_powers.txt">Table of a(n) and its mate for n=1..36</a>

%H K. Oséki, <a href="http://dx.doi.org/10.3792/pja/1195523903">A problem of number theory</a>, Proceedings of the Japan Academy 36 (1960), 578-587.

%e a(1) is amicably paired to 136, because 1^3 + 3^3 + 6^3 = 244 and 2^3 + 4^3 + 4^3 = 136.

%o (Python)

%o from itertools import count, combinations_with_replacement, islice

%o def A262092_gen(): # generator of terms

%o     for m in count(2):

%o         for c in combinations_with_replacement(range(10),m+1):

%o             n = sum(d**m for d in c)

%o             r = sum(int(q)**m for q in str(n))

%o             rlist = sorted(int(d) for d in str(r))

%o             rlist = [0]*(m+1-len(rlist))+rlist

%o             if n < r and rlist == list(c):

%o                 yield r

%o A262092_list = list(islice(A262092_gen(),10)) # _Chai Wah Wu_, Dec 31 2021

%Y A262091 has the smaller element of each pair.

%K nonn,base

%O 1,1

%A _Don Knuth_, Sep 10 2015

%E Definition clarified by _Chai Wah Wu_, Jan 04 2016