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.
a(1) = A230477(3) = 5104 = 1^3 + 12^3 + 15^3 = 2^3 + 10^3 + 16^3 = 9^3 + 10^3 + 15^3. - _Jonathan Sondow_, Oct 24 2013
Select[ Range[ 50000], 2 < Length @ Cases[ PowersRepresentations[#, 3, 3], {?Positive, ?Positive, A008917%20by%20_Jonathan%20Sondow">?Positive}] &] (* adapted from Alcover's program for A008917 by _Jonathan Sondow, Oct 24 2013 *)
is(n)=k=ceil((n-2)^(1/3)); d=0; for(a=1,k,for(b=a,k,for(c=b,k,if(a^3+b^3+c^3==n,d++))));d n=3;while(n<50000,if(is(n)>=3,print1(n,", "));n++) \\ Derek Orr, Aug 27 2015
314712 = 4^3 + 6^3 + 68^3
= 5^3 + 24^3 + 67^3
= 6^3 + 30^3 + 66^3
= 31^3 + 41^3 + 60^3
= 36^3 + 48^3 + 54^3
so 314712 is a term of this sequence.
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,50)]
for pos in cwr(power_terms,3):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 5])
for x in range(len(rets)):
print(rets[x])
3663 = 1^3 + 10^3 + 11^3 + 11^3
= 2^3 + 4^3 + 6^3 + 15^3
= 2^3 + 9^3 + 9^3 + 13^3
= 4^3 + 7^3 + 8^3 + 14^3
so 3663 is a term.
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,50)]
for pos in cwr(power_terms,4):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 4])
for x in range(len(rets)):
print(rets[x])
44946 is a term because 44946 = 7^3 + 12^3 + 35^3 = 9^3 + 17^3 + 34^3 = 11^3 + 24^3 + 31^3 = 16^3 + 17^3 + 33^3.
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,50)]
for pos in cwr(power_terms,3):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 4])
for x in range(len(rets)):
print(rets[x])
20621042 is a member of this sequence because 20621042 = 5^4 + 54^4 + 59^4 = 10^4 + 51^4 + 61^4 = 25^4 + 46^4 + 63^4 = 26^4 + 39^4 + 65^4
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1,50)]
for pos in cwr(power_terms,3):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 4])
for x in range(len(rets)):
print(rets[x])
a(1) = 36 = 1^3 + 2^3 + 3^3. a(2) = 1009 = 1^3 + 2^3 + 10^3 = 4^3 + 6^3 + 9^3. a(3) = 12384 = 1^3 + 6^3 + 23^3 = 2^3 + 12^3 + 22^3 = 15^3 + 16^3 + 17^3.
Monitor[Do[k=1;While[Length@Union@Flatten[p=PowersRepresentations[k,3,3]]!=n*3||Length@p!=n||MemberQ[Flatten@p,0],k++];Print@k,{n,10}],k] (* Giorgos Kalogeropoulos, Sep 03 2021 *)
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