A262615
Amicable digital pairs: A262091 and A262092 interleaved.
Original entry on oeis.org
136, 244, 919, 1459, 2178, 6514, 58618, 76438, 89883, 157596, 63804, 313625, 2755907, 6586433, 8139850, 9057586, 144839908, 1043820406, 277668893, 756738746, 304162700, 344050075, 4370652168, 11346057072, 21914086555935085, 37878721692554416, 187864919457180831, 375609204308055082, 13397885590701080090, 40091536165423401387
Offset: 1
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.
Original entry on oeis.org
244, 1459, 6514, 76438, 157596, 313625, 6586433, 9057586, 1043820406, 756738746, 344050075, 11346057072, 37878721692554416, 375609204308055082, 40091536165423401387, 244405038116365070846858, 183144838903847612823687, 2307549584666787613389634
Offset: 1
a(1) is amicably paired to 136, because 1^3 + 3^3 + 6^3 = 244 and 2^3 + 4^3 + 4^3 = 136.
A262091 has the smaller element of each pair.
-
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
A264951
Amicable digital numbers.
Original entry on oeis.org
136, 244, 919, 1459, 2178, 6514, 58618, 63804, 76438, 89883, 157596, 313625, 2755907, 6586433, 8139850, 9057586, 144839908, 277668893, 304162700, 344050075, 756738746, 1043820406, 4370652168, 11346057072, 21914086555935085, 37878721692554416, 187864919457180831, 375609204308055082, 13397885590701080090, 40091536165423401387
Offset: 1
- K. Oséki, A problem of number theory, Proceedings of the Japan Academy 36 (1960), 578-587.
A264958
Amicable digital pair: the pairs from A262615 ordered by their smallest member.
Original entry on oeis.org
136, 244, 919, 1459, 2178, 6514, 58618, 76438, 63804, 313625, 89883, 157596, 2755907, 6586433, 8139850, 9057586, 144839908, 1043820406, 277668893, 756738746, 304162700, 344050075, 4370652168, 11346057072, 21914086555935085, 37878721692554416, 187864919457180831, 375609204308055082, 13397885590701080090, 40091536165423401387
Offset: 1
Showing 1-4 of 4 results.
Comments