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

Author

Amiram Eldar, Jun 04 2020

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

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

Programs

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