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

Author

N. J. A. Sloane, Nov 25 2002

Keywords

• nonn
• easy

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.

Crossrefs

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

Different from A070049.

Programs

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 *)

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

Extensions

More terms from Vladeta Jovovic, Nov 25 2002