A344242 -id:A344242 - cp's OEIS frontend

A344193 Numbers that are the sum of four fourth powers in exactly two ways.

259, 2674, 2689, 2754, 2929, 3298, 3969, 4144, 4209, 5074, 6579, 6594, 6659, 6769, 6834, 7203, 7874, 8194, 8979, 9154, 9234, 10113, 10674, 11298, 12673, 12913, 13139, 14674, 14689, 14754, 16563, 16643, 16818, 17187, 17234, 17299, 17314, 17858, 18963, 19699, 20658, 20739, 20979, 21154, 21219, 21329, 21363

Offset: 1

David Consiglio, Jr., May 11 2021

nonn

Differs from A309763 at term 32 because 16578 = 1^4 + 2^4 + 9^4 + 10^4 = 2^4 + 5^4 + 6^4 + 11^4 = 3^4 + 7^4 + 8^4 + 10^4

			2689 is a member of this sequence because 2689 = 2^4 + 2^4 + 4^4 + 7^4 = 2^4 + 3^4 + 6^4 + 6^4

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

Cf. A025404, A309763, A344189, A344192, A344237, A344242, A344645.

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 == 2])
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])

A344244 Numbers that are the sum of five fourth powers in exactly three ways.

Original entry on oeis.org

4225, 6610, 6850, 9170, 9235, 9490, 11299, 12929, 14209, 14690, 14755, 14770, 15314, 16579, 16594, 16659, 16834, 17203, 17235, 17315, 17859, 17874, 17939, 18785, 18850, 18979, 19154, 19700, 19715, 20674, 21250, 21330, 21364, 21410, 21954, 23139, 23795, 24754, 25810, 26578, 28610, 28930, 29330, 29699

Offset: 1

David Consiglio, Jr., May 12 2021

nonn

Differs from A344243 at term 31 because 20995 = 1^4 + 1^4 + 1^4 + 4^4 + 12^4 = 2^4 + 3^4 + 3^4 + 3^4 + 12^4 = 2^4 + 6^4 + 9^4 + 9^4 + 9^4 = 4^4 + 6^4 + 7^4 + 7^4 + 11^4

			6850 is a member of this sequence because 6850 =  = 1^4 + 2^4 + 2^4 + 4^4 + 9^4 = 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 3^4 + 3^4 + 6^4 + 6^4 + 8^4

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

Cf. A342688, A343705, A344237, A344242, A344243, A344355, A345815.

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,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])

A344353 Numbers that are the sum of four fourth powers in exactly four ways.

Original entry on oeis.org

236674, 282018, 300834, 334818, 478338, 637794, 650034, 650658, 708483, 708834, 729938, 789378, 816578, 832274, 849954, 941859, 989043, 1042083, 1045539, 1099203, 1099458, 1102258, 1179378, 1243074, 1257954, 1283874, 1323234, 1334979, 1339074, 1342979, 1352898, 1357059, 1379043, 1518578

Offset: 1

David Consiglio, Jr., May 15 2021

nonn

Differs from A344352 at term 52 because 2147874 = 2^4 + 14^4 + 31^4 + 33^4 = 4^4 + 23^4 + 27^4 + 34^4 = 7^4 + 21^4 + 28^4 + 34^4 = 12^4 + 17^4 + 29^4 + 34^4 = 14^4 + 18^4 + 19^4 + 37^4.

			300834 is a term of this sequence because 300834 = 1^4 + 4^4 + 12^4 + 23^4 = 1^4 + 16^4 + 18^4 + 19^4 = 3^4 + 6^4 + 18^4 + 21^4 = 7^4 + 14^4 + 16^4 + 21^4.

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

Cf. A343972, A344242, A344278, A344352, A344355, A344357.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1,200)]
count = 1
for pos in cwr(power_terms,4):
    tot = sum(pos)
    keep[tot] += 1
    count += 1
rets = sorted([k for k,v in keep.items() if v == 4])
for x in range(len(rets)):
    print(rets[x])

A344240 Numbers that are the sum of three fourth powers in exactly three ways.

Original entry on oeis.org

811538, 1733522, 2798978, 3750578, 4614722, 6573938, 7303842, 8878898, 12771458, 12984608, 13760258, 14677362, 15601698, 16196193, 17868242, 21556178, 22349522, 25190802, 25589858, 27736352, 29969282, 41532498, 44048498, 44783648, 45182018, 50944418, 54894242, 57052562, 59165442, 60009248

Offset: 1

David Consiglio, Jr., May 12 2021

nonn

Differs from A344239 at term 6 because 5978882 = 3^4 + 40^4 + 43^4 = 8^4 + 37^4 + 45^4 = 15^4 + 32^4 + 47^4 = 23^4 + 25^4 + 48^4

			2798978 is a member of this sequence because 2798978 = 6^4 + 31^4 + 37^4 = 9^4 + 29^4 + 38^4 = 13^4 + 26^4 + 39^4

David Consiglio, Jr., Table of n, a(n) for n = 1..5129

Cf. A025397, A344192, A344239, A344242, A344278.

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 == 3])
for x in range(len(rets)):
    print(rets[x])

A025405 Numbers that are the sum of 4 positive cubes in exactly 3 ways.

Original entry on oeis.org

1225, 1521, 1582, 1584, 1738, 1764, 2009, 2249, 2366, 2415, 2422, 2457, 2459, 2485, 2520, 2539, 2753, 2763, 2790, 2799, 3008, 3094, 3185, 3187, 3213, 3248, 3276, 3392, 3456, 3458, 3465, 3572, 3582, 3600, 3607, 3626, 3656, 3717, 3736, 3753, 3815, 3941

Offset: 1

David W. Wilson

nonn

Cf. A025359, A025397, A025404, A025407, A343705, A343972, A344242.

{n: A025457(n) = 3}. - R. J. Mathar, Jun 15 2018

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A344193 Numbers that are the sum of four fourth powers in exactly two ways.

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

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A344244 Numbers that are the sum of five fourth powers in exactly three ways.

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A344353 Numbers that are the sum of four fourth powers in exactly four ways.

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A344240 Numbers that are the sum of three fourth powers in exactly three ways.

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A025405 Numbers that are the sum of 4 positive cubes in exactly 3 ways.

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