cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A344380 Complement of A344378 in A172186.

Original entry on oeis.org

6, 14, 38, 42, 57, 65, 70, 93, 106, 114, 118, 138, 154, 158, 182, 186, 190, 205, 210, 217, 218, 222, 266, 277, 281, 285, 309, 326, 334, 366, 381, 390, 393, 394, 397, 398, 401, 406, 434, 457, 469, 473, 478, 493, 498, 505, 518, 542, 561, 570, 581, 606, 614, 618
Offset: 1

Views

Author

René Gy, May 16 2021

Keywords

Comments

Terms belong to A172186 but not to A344378. Even though a(n)*(a(n)+1)*(2*a(n)+1) is squarefree, Sum_{j=1..a(n)} j^(2k) always has a prime divisor which is smaller than 2*a(n)+3, whatever k. For the integers m such that m*(m+1)*(2*m+1) is nonsquarefree, Sum_{j=1..m} j^(2k) always has a prime divisor which is smaller than 2*m+3, whatever k, because it is divisible by any prime p such that p^2 divides m*(m+1)*(2*m+1).

Examples

			14 belongs to the sequence, because it is squarefree, and Sum_{j=1..14} j^(2k) is always divisible by 29 when 14 does not divide k, and when 14 divides k, it is divisible by 13 or by 7.

Links

Crossrefs

Cf. A172186, A344378.

Extensions

More terms added and incorrect Mathematica program removed by Jinyuan Wang, Mar 07 2025
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