A345337 -id:A345337 - cp's OEIS frontend

A342687 Numbers that are the sum of five fifth powers in three or more ways.

13124675, 28055699, 50043937, 52679923, 53069024, 55097976, 57936559, 60484744, 62260463, 62445305, 70211956, 73133026, 79401728, 80368962, 84766210, 88512249, 93288865, 98824300, 106993391, 113055482, 117173891, 120968132, 123383875, 126416258, 131106051, 131529588, 132022925

Offset: 1

David Consiglio, Jr., May 18 2021

nonn

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Cf. A342685, A342688, A344243, A344518, A345337, A345604.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 500)]
for pos in cwr(power_terms, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 3])
for x in range(len(rets)):
    print(rets[x])

A344241 Numbers that are the sum of four fourth powers in three or more ways.

Original entry on oeis.org

16578, 43234, 49329, 53218, 54978, 57154, 93393, 106354, 107649, 108754, 138258, 151219, 160434, 168963, 173539, 177699, 178738, 181138, 183603, 185298, 195378, 195859, 196418, 197154, 197778, 201683, 202419, 209763, 211249, 216594, 217138, 223074, 234274, 235554, 235569, 236674, 237249, 237699

Offset: 1

David Consiglio, Jr., May 12 2021

nonn

			49329 = 2^4 + 2^4 + 12^4 + 13^4
      = 4^4 + 8^4 +  9^4 + 14^4
      = 6^4 + 9^4 + 12^4 + 12^4
so 49329 is a term of this sequence.

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Cf. A025407, A309763, A344239, A344242, A344243, A344352, A345337.

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,4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 3])
for x in range(len(rets)):
    print(rets[x])

A344644 Numbers that are the sum of four fifth powers in two or more ways.

Original entry on oeis.org

51445, 876733, 1646240, 3558289, 4062500, 5687000, 7962869, 8227494, 9792364, 9924675, 10908544, 12501135, 15249850, 18317994, 18804544, 20611151, 20983875, 21297837, 23944908, 24201342, 24598407, 27806867, 28055456, 29480343, 31584102, 32557875, 32814683, 35469555, 40882844, 45177175

Offset: 1

David Consiglio, Jr., May 25 2021

nonn

			1646240 is a term because 1646240 = 9^5 + 15^5 + 15^5 + 15^5 = 11^5 + 13^5 + 13^5 + 17^5

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Cf. A003349, A309763, A342685, A344645, A345010, A345337.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 500)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 2])
for x in range(len(rets)):
    print(rets[x])

cp's OEIS Frontend

A342687 Numbers that are the sum of five fifth powers in three or more ways.

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A344241 Numbers that are the sum of four fourth powers in three or more ways.

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A344644 Numbers that are the sum of four fifth powers in two or more ways.

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