A345636 -id:A345636 - cp's OEIS frontend

A345597 Numbers that are the sum of ten fourth powers in four or more ways.

1620, 2660, 2725, 2740, 2835, 2855, 2870, 2900, 2915, 2920, 2935, 2950, 2965, 2980, 3000, 3015, 3030, 3045, 3095, 3110, 3160, 3175, 3190, 3205, 3220, 3240, 3255, 3270, 3285, 3335, 3350, 3415, 3430, 3445, 3460, 3479, 3510, 3525, 3544, 3559, 3574, 3589, 3639

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			2660 is a term because 2660 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 6^4 + 6^4 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4.

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A345552, A345588, A345596, A345598, A345636, A345856.

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, 1000)]
for pos in cwr(power_terms, 10):
    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])

A345621 Numbers that are the sum of nine fifth powers in four or more ways.

Original entry on oeis.org

55542, 120350, 143507, 167241, 182549, 192233, 202890, 326685, 327986, 328247, 329028, 329809, 333257, 351722, 358474, 358968, 359210, 359538, 359813, 365404, 367071, 367313, 374034, 374846, 375627, 376619, 377158, 379259, 381157, 383910, 384765, 390396

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			120350 is a term because 120350 = 1^5 + 3^5 + 4^5 + 5^5 + 7^5 + 7^5 + 7^5 + 8^5 + 8^5 = 1^5 + 3^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 8^5 = 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 7^5 + 7^5 + 7^5 + 9^5 = 2^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 6^5 + 8^5 + 9^5.

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A345588, A345612, A345620, A345622, A345636, A346339.

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, 1000)]
for pos in cwr(power_terms, 9):
    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])

A345635 Numbers that are the sum of ten fifth powers in three or more ways.

Original entry on oeis.org

8194, 21940, 52419, 52450, 52481, 52661, 52692, 52903, 53442, 53473, 53684, 54465, 54520, 54551, 54582, 54762, 54793, 55004, 55543, 55574, 55691, 55722, 55785, 55933, 56566, 56714, 57644, 57675, 57886, 58667, 58815, 60194, 60225, 60436, 60768, 61217, 62295

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			21940 is a term because 21940 = 1^5 + 2^5 + 2^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 = 1^5 + 3^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 6^5 = 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5.

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A345596, A345620, A345634, A345636, A346348.

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, 1000)]
for pos in cwr(power_terms, 10):
    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])

A345637 Numbers that are the sum of ten fifth powers in five or more ways.

Original entry on oeis.org

200009, 220350, 235658, 329271, 329810, 330052, 359211, 359453, 359498, 360298, 367314, 368529, 374519, 374847, 375089, 375870, 376620, 376651, 377159, 377643, 380283, 382622, 384395, 384934, 387035, 388933, 391736, 392064, 392095, 392275, 392306, 392339

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			220350 is a term because 220350 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 3^5 + 9^5 + 11^5 = 1^5 + 3^5 + 4^5 + 5^5 + 7^5 + 7^5 + 7^5 + 8^5 + 8^5 + 10^5 = 1^5 + 3^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 8^5 + 10^5 = 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 7^5 + 7^5 + 7^5 + 9^5 + 10^5 = 2^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 6^5 + 8^5 + 9^5 + 10^5.

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A345598, A345622, A345636, A345638, A346350.

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, 1000)]
for pos in cwr(power_terms, 10):
    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])

A346349 Numbers that are the sum of ten fifth powers in exactly four ways.

Original entry on oeis.org

55543, 55574, 55785, 56566, 58667, 63318, 72349, 73002, 85186, 86506, 87287, 87529, 88310, 103134, 111498, 113599, 114591, 118250, 119031, 120351, 120382, 120593, 121374, 123475, 128126, 134475, 134878, 135201, 137157, 142008, 142219, 143000, 143211, 143506

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345636 at term 92 because 200009 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5 + 10^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 8^5 + 10^5 = 1^5 + 3^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 8^5 + 10^5 = 2^5 + 2^5 + 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 8^5 + 8^5 + 9^5 = 1^5 + 2^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5.

			55543 is a term because 55543 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 5^5 + 7^5 + 7^5 + 7^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5.

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A345636, A345856, A346339, A346348, A346350.

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, 1000)]
for pos in cwr(power_terms, 10):
    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])

cp's OEIS Frontend

A345597 Numbers that are the sum of ten fourth powers in four or more ways.

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A345621 Numbers that are the sum of nine fifth powers in four or more ways.

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A345635 Numbers that are the sum of ten fifth powers in three or more ways.

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A345637 Numbers that are the sum of ten fifth powers in five or more ways.

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A346349 Numbers that are the sum of ten fifth powers in exactly four ways.

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