

A335389


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


0



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
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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 A020323 A036322
Adjacent sequences: A335386 A335387 A335388 * A335390 A335391 A335392


KEYWORD

nonn


AUTHOR

Amiram Eldar, Jun 04 2020


STATUS

approved



