A228541 -id:A228541

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A228556

Sums of two coprime positive cubes that are also sums of two coprime positive fifth powers.

+10
3

2, 32769, 14348908, 14381675, 1073741825, 1088090731, 30517578126, 30517610893, 30531927032, 31591319949, 43977108474, 470184984577, 500702562701, 4747561509944, 4747561542711, 4747575858850, 4748635251767, 4778079088068, 5217746494519

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Every term greater than 2 has at least one prime factor of the form 30*k + 1 and therefore is in A228541.

LINKS

Arkadiusz Wesolowski and Chai Wah Wu, Table of n, a(n) for n = 1..103 (terms n = 1..24 from Arkadiusz Wesolowski)

Index to sequences related to sums of cubes

FORMULA

A202679 INTERSECT A228542.

EXAMPLE

14381675 is in the sequence since 32^3 + 243^3 = 8^5 + 27^5 = 14381675 and (32, 243) = (8, 27) = 1.

CROSSREFS

Cf. A035046, A202679, A228541, A228542.

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Aug 25 2013

STATUS

approved

A374365

Numbers m such that abs(Sum_{k=1..m} [k|m]*A008683(k)*(-1)^(2*k/5)) = 0.

+10
0

11, 22, 31, 33, 41, 44, 55, 61, 62, 66, 71, 77, 82, 88, 93, 99, 101, 110, 121, 122, 123, 124, 131, 132, 142, 143, 151, 154, 155, 164, 165, 176, 181, 183, 186, 187, 191, 198, 202, 205, 209, 211, 213, 217, 220, 231, 241, 242, 244, 246, 248, 251, 253, 262, 264, 271

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Conjecture: Numbers having a prime factor congruent to 1 mod 10.

LINKS

Table of n, a(n) for n=1..56.

MATHEMATICA

nn = 274; Flatten[Position[ParallelTable[Abs[Sum[If[Mod[n, k] == 0, 1, 0]*((-1)^( 2*k/5))*MoebiusMu[k], {k, 1, n}]], {n, 1, nn}], 0]]