A335389 Numbers k such that k and k+1 are both antiharmonic numbers (A020487).

49, 324, 1024, 1444, 1681, 2600, 9800, 265225, 332928, 379456, 421200, 1940449, 4198400, 4293184, 4739328, 8346320, 11309768, 27050400, 65918161, 203694425, 384199200, 418488849, 546717924, 2239277041, 2687489280, 4866742025, 5783450400, 6933892900, 7725003664

Offset

1,1

Comments

Terms of this sequence k such that k and k+1 are both nonsquares (A227771) are 203694425, 4866742025, ...

Can two consecutive numbers be both primitive antiharmonic numbers (A228023)? Numbers k such that k and k+2 are both primitive antiharmonic numbers exist - the first two are 38246258 and 344321280.

Links

Table of n, a(n) for n=1..29.

Example

49 is a term since both 49 and 50 are antiharmonic: sigma_2(49)/sigma(49) = 43 and sigma_2(50)/sigma(50) = 35 are both integers.

Mathematica

antihQ[n_] := Divisible[DivisorSigma[2, n], DivisorSigma[1, n]]; seq = {}; q1 = antihQ[1];  Do[q2 = antihQ[n]; If[q1 && q2, AppendTo[seq, n - 1]]; q1 = q2, {n, 2, 2 * 10^6}]; seq

Crossrefs

Cf. A000203, A001157, A020487, A227771, A228023.

Sequence in context: A245033 A340124 A017474 * A036318 A365206 A020323

Adjacent sequences: A335386 A335387 A335388 * A335390 A335391 A335392

Keyword

nonn

Author

Amiram Eldar, Jun 04 2020

Status

approved