A262092 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.

244, 1459, 6514, 76438, 157596, 313625, 6586433, 9057586, 1043820406, 756738746, 344050075, 11346057072, 37878721692554416, 375609204308055082, 40091536165423401387, 244405038116365070846858, 183144838903847612823687, 2307549584666787613389634

Offset: 1

Author

Don Knuth, Sep 10 2015

Keywords

• nonn
• base

Examples

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

Links

• D. Knuth, Table of a(n) and its mate for n=1..36
• K. Oséki, A problem of number theory, Proceedings of the Japan Academy 36 (1960), 578-587.

Crossrefs

A262091 has the smaller element of each pair.

Programs

Python

from itertools import count, combinations_with_replacement, islice
def A262092_gen(): # generator of terms
    for m in count(2):
        for c in combinations_with_replacement(range(10),m+1):
            n = sum(d**m for d in c)
            r = sum(int(q)**m for q in str(n))
            rlist = sorted(int(d) for d in str(r))
            rlist = [0]*(m+1-len(rlist))+rlist
            if n < r and rlist == list(c):
                yield r
A262092_list = list(islice(A262092_gen(),10)) # Chai Wah Wu, Dec 31 2021

Extensions

Definition clarified by Chai Wah Wu, Jan 04 2016