A076871 Sum of two powerful numbers (definition (1), A001694).

2, 5, 8, 9, 10, 12, 13, 16, 17, 18, 20, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 37, 40, 41, 43, 44, 45, 48, 50, 52, 53, 54, 57, 58, 59, 61, 63, 64, 65, 68, 72, 73, 74, 76, 80, 81, 82, 85, 88, 89, 90, 91, 96, 97, 98, 99, 100, 101, 104, 106, 108, 109, 112, 113, 116, 117

Offset

1,1

Comments

Complement of A085253. - Reinhard Zumkeller, Jun 23 2003

References

Aleksandar Ivić, The Riemann Zeta-Function, Wiley, NY, 1985, see p. 439.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Valentin Blomer, Binary quadratic forms with large discriminants and sums of two squareful numbers II, Journal of the London Mathematical Society 71:1 (2005), pp. 69-84.

Alexander Kalmynin and Segei Konyagin, Large gaps between sums of two squareful numbers, arXiv:2303.14833 [math.NT], 2023.

Eric Weisstein's World of Mathematics, Powerful Number.

Formula

A085252(a(n)) > 0. - Reinhard Zumkeller, Jun 23 2003

Blomer shows that there are x/log^k x sums of two powerful numbers up to x, where k = 0.20629947... is A261883. - Charles R Greathouse IV, Sep 04 2015

Mathematica

With[{m = 120}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; Select[Union[Plus @@@ Tuples[pow, {2}]], # <= m &]] (* Amiram Eldar, Jan 30 2023 *)

Crossrefs

Cf. A001694, A076872, A085252, A085253, A261883.

Different from A070049.

Sequence in context: A288730 A276784 A153129 * A070049 A085254 A274035

Adjacent sequences: A076868 A076869 A076870 * A076872 A076873 A076874

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 25 2002

Extensions

More terms from Vladeta Jovovic, Nov 25 2002

Status

approved