A335251 Numbers k such that k and k+1 have the same unitary abundance (A129468).

1, 20, 35, 143, 208, 2623, 5183, 27796, 11177983, 69677008, 920158207, 1099508482048

Offset: 1

Author

Amiram Eldar, May 28 2020

Keywords

• nonn
• more

Comments

Are there any unitary abundant numbers (A034683) in this sequence?

a(12) > 10^11.

a(13) > 8*10^12. Also terms: 2^36 * 68719644673, 2^48 * 281474901625261, 2^64 * 18446632096776339457. - Giovanni Resta, May 29 2020

Examples

			1 is a term since 1 and 2 have the same unitary abundance: A129468(1) = usigma(1) - 2*1 = 1 - 2 = -1, and A129468(2) = usigma(2) - 2*2 = 3 - 4 = -1.
		

Crossrefs

Cf. A034448, A034683, A129468, A129487, A331412, A335252.

Programs

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); udef[n_] := 2*n - usigma[n]; Select[Range[30000], udef[#] == udef[# + 1] &]

Extensions

a(12) from Giovanni Resta, May 29 2020