A346365 -id:A346365 - cp's OEIS frontend

A345822 Numbers that are the sum of six fourth powers in exactly ten ways.

122915, 151556, 161475, 162755, 173075, 183620, 185315, 199106, 199940, 201875, 202275, 204275, 204340, 204595, 206115, 207395, 209795, 211075, 213731, 217826, 217891, 218515, 221250, 223955, 224180, 225875, 226595, 227186, 228035, 236195, 237796, 237890

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345567 at term 8 because 197795 = 1^4 + 2^4 + 5^4 + 6^4 + 16^4 + 19^4 = 1^4 + 2^4 + 7^4 + 11^4 + 12^4 + 20^4 = 1^4 + 2^4 + 10^4 + 12^4 + 17^4 + 17^4 = 2^4 + 4^4 + 7^4 + 9^4 + 13^4 + 20^4 = 2^4 + 11^4 + 13^4 + 14^4 + 15^4 + 16^4 = 3^4 + 6^4 + 6^4 + 9^4 + 13^4 + 20^4 = 3^4 + 6^4 + 7^4 + 14^4 + 15^4 + 18^4 = 4^4 + 9^4 + 11^4 + 12^4 + 15^4 + 18^4 = 7^4 + 7^4 + 14^4 + 14^4 + 15^4 + 16^4.

			151556 is a term because 151556 = 1^4 + 2^4 + 2^4 + 9^4 + 11^4 + 19^4 = 1^4 + 2^4 + 3^4 + 7^4 + 16^4 + 17^4 = 1^4 + 8^4 + 11^4 + 12^4 + 13^4 + 17^4 = 2^4 + 3^4 + 7^4 + 8^4 + 11^4 + 19^4 = 3^4 + 3^4 + 3^4 + 4^4 + 12^4 + 19^4 = 3^4 + 4^4 + 11^4 + 11^4 + 14^4 + 17^4 = 3^4 + 4^4 + 13^4 + 13^4 + 13^4 + 16^4 = 4^4 + 6^4 + 9^4 + 9^4 + 9^4 + 19^4 = 4^4 + 7^4 + 11^4 + 11^4 + 11^4 + 18^4 = 4^4 + 8^4 + 9^4 + 13^4 + 13^4 + 17^4.

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

Cf. A341898, A345567, A345772, A345821, A345832, A346365.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 10])
    for x in range(len(rets)):
        print(rets[x])

A346259 Numbers that are the sum of seven fifth powers in exactly ten ways.

Original entry on oeis.org

134581976, 189642309, 219063107, 235438301, 252277376, 275782407, 300919884, 308188849, 309631268, 315635200, 327287951, 335530174, 342030094, 358852218, 379913293, 384699424, 387538625, 391133568, 395423876, 405307926, 421322507, 423673757, 425588250

Offset: 1

David Consiglio, Jr., Jul 12 2021

nonn

Differs from A345643 at term 7 because 281935070 = 17^5 + 17^5 + 18^5 + 21^5 + 23^5 + 26^5 + 48^5 = 7^5 + 17^5 + 20^5 + 23^5 + 24^5 + 32^5 + 47^5 = 7^5 + 13^5 + 13^5 + 26^5 + 30^5 + 36^5 + 45^5 = 1^5 + 13^5 + 21^5 + 21^5 + 33^5 + 37^5 + 44^5 = 6^5 + 7^5 + 13^5 + 31^5 + 34^5 + 36^5 + 43^5 = 4^5 + 8^5 + 16^5 + 29^5 + 31^5 + 41^5 + 41^5 = 6^5 + 8^5 + 12^5 + 28^5 + 37^5 + 38^5 + 41^5 = 3^5 + 6^5 + 15^5 + 32^5 + 35^5 + 38^5 + 41^5 = 7^5 + 24^5 + 25^5 + 32^5 + 34^5 + 37^5 + 41^5 = 13^5 + 20^5 + 21^5 + 34^5 + 35^5 + 36^5 + 41^5 = 8^5 + 24^5 + 26^5 + 31^5 + 31^5 + 40^5 + 40^5.

			134581976 is a term because 134581976 = 1^5 + 14^5 + 17^5 + 18^5 + 26^5 + 31^5 + 39^5 = 1^5 + 1^5 + 10^5 + 12^5 + 19^5 + 35^5 + 38^5 = 8^5 + 11^5 + 12^5 + 17^5 + 27^5 + 33^5 + 38^5 = 3^5 + 12^5 + 12^5 + 21^5 + 28^5 + 32^5 + 38^5 = 4^5 + 11^5 + 13^5 + 22^5 + 24^5 + 36^5 + 36^5 = 5^5 + 6^5 + 19^5 + 20^5 + 24^5 + 36^5 + 36^5 = 1^5 + 4^5 + 21^5 + 21^5 + 29^5 + 34^5 + 36^5 = 1^5 + 8^5 + 14^5 + 23^5 + 32^5 + 32^5 + 36^5 = 6^5 + 25^5 + 25^5 + 25^5 + 29^5 + 30^5 + 36^5 = 12^5 + 20^5 + 21^5 + 26^5 + 28^5 + 34^5 + 35^5.

Sean A. Irvine, Table of n, a(n) for n = 1..4377

Cf. A345643, A345832, A346286, A346335, A346365.

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, 7):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 10])
    for x in range(len(rets)):
        print(rets[x])

A346364 Numbers that are the sum of six fifth powers in exactly nine ways.

Original entry on oeis.org

9085584992, 16933805856, 37377003050, 39254220544, 41066625600, 41485873792, 42149876800, 43828403850, 44180505600, 45902654525, 48588434400, 52005184992, 53536896864, 54156285568, 56229189632, 57088402525, 59954496800, 63432407850, 66188522400, 66507304800

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

This sequence differs from A345723:
55302546200 = 34^5 + 38^5 + 50^5 +  57^5 +  95^5 + 136^5
            = 23^5 + 49^5 + 61^5 +  69^5 + 107^5 + 131^5
            = 24^5 + 37^5 + 63^5 +  81^5 + 104^5 + 131^5
            = 21^5 + 35^5 + 60^5 +  94^5 + 100^5 + 130^5
            = 57^5 + 60^5 + 71^5 +  75^5 + 109^5 + 128^5
            = 19^5 + 37^5 + 56^5 +  96^5 + 104^5 + 128^5
            = 35^5 + 41^5 + 53^5 +  69^5 + 115^5 + 127^5
            = 16^5 + 49^5 + 53^5 +  83^5 + 112^5 + 127^5
            = 35^5 + 37^5 + 40^5 +  88^5 + 119^5 + 121^5
            = 11^5 + 24^5 + 71^5 + 104^5 + 109^5 + 121^5,
so 55302546200 is in A345723, but is not in this sequence.

			9085584992 = 24^5 + 38^5 + 42^5 + 48^5 + 54^5 + 96^5
           = 21^5 + 34^5 + 38^5 + 43^5 + 74^5 + 92^5
           =  8^5 + 34^5 + 38^5 + 62^5 + 68^5 + 92^5
           = 18^5 + 18^5 + 44^5 + 64^5 + 66^5 + 92^5
           = 13^5 + 18^5 + 51^5 + 64^5 + 64^5 + 92^5
           =  8^5 + 38^5 + 41^5 + 47^5 + 79^5 + 89^5
           =  5^5 + 23^5 + 29^5 + 45^5 + 85^5 + 85^5
           =  8^5 + 23^5 + 41^5 + 64^5 + 82^5 + 84^5
           = 12^5 + 18^5 + 38^5 + 72^5 + 78^5 + 84^5,
so 9085584992 is a term.

Sean A. Irvine, Table of n, a(n) for n = 1..549

Cf. A345723, A345821, A346286, A346363, A346365.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 9])
    for x in range(len(rets)):
        print(rets[x])

A344196 Numbers that are the sum of six fifth powers in ten or more ways.

Original entry on oeis.org

55302546200, 89999127392, 96110537743, 104484239200, 120492759200, 121258798144, 127794946400, 133364991375, 135030535200, 136156575744, 151305014432, 155434423925, 174388570400, 177099008000, 179272687000, 180336745600, 182844944832, 184948721056, 187873845500

Offset: 1

David Consiglio, Jr., Jun 25 2021

nonn

			89999127392 =  4^5 + 36^5 + 39^5 +  40^5 +  90^5 + 153^5
            =  8^5 + 21^5 + 90^5 + 109^5 + 119^5 + 135^5
            =  8^5 + 28^5 + 98^5 + 102^5 + 104^5 + 142^5
            = 10^5 + 38^5 + 74^5 + 102^5 + 118^5 + 140^5
            = 13^5 + 51^5 + 64^5 +  98^5 + 112^5 + 144^5
            = 18^5 + 44^5 + 66^5 +  98^5 + 112^5 + 144^5
            = 18^5 + 52^5 + 72^5 +  78^5 + 118^5 + 144^5
            = 28^5 + 60^5 + 63^5 +  65^5 + 124^5 + 142^5
            = 36^5 + 53^5 + 62^5 +  63^5 + 129^5 + 139^5
            = 39^5 + 41^5 + 64^5 +  91^5 +  98^5 + 149^5
so 89999127392 is a term.

Sean A. Irvine, Table of n, a(n) for n = 1..61

Cf. A345567, A345643, A345723, A346365.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 10])
    for x in range(len(rets)):
        print(rets[x])

cp's OEIS Frontend

A345822 Numbers that are the sum of six fourth powers in exactly ten ways.

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A346259 Numbers that are the sum of seven fifth powers in exactly ten ways.

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A346364 Numbers that are the sum of six fifth powers in exactly nine ways.

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A344196 Numbers that are the sum of six fifth powers in ten or more ways.

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