A335252 Numbers k such that k and k+2 have the same unitary abundance (A129468).

12, 63, 117, 323, 442, 1073, 1323, 1517, 3869, 5427, 6497, 12317, 18419, 35657, 69647, 79919, 126869, 133787, 151979, 154007, 163332, 181427, 184619, 333797, 404471, 439097, 485237, 581129, 621497, 825497, 1410119, 2696807, 3077909, 3751619, 5145341, 6220607

Offset

1,1

Comments

Are 12, 442 and 163332 the only even terms?

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

No further even terms up to 10^13. - Giovanni Resta, May 30 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..300

Example

12 is a term since 12 and 14 have the same unitary abundance: A129468(12) = usigma(12) - 2*12 = 20 - 24 = -4, and A129468(14) = usigma(14) - 2*14 = 24 - 28 = -4.

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); udef[n_] := 2*n - usigma[n]; Select[Range[10^5], udef[#] == udef[# + 2] &]

Crossrefs

The unitary version of A330901.

Cf. A034448, A034683, A129468, A129487, A335251.

Sequence in context: A196335 A349159 A092224 * A212509 A212249 A309372

Adjacent sequences: A335249 A335250 A335251 * A335253 A335254 A335255

Keyword

nonn

Author

Amiram Eldar, May 28 2020

Status

approved