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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 8 07:17 EST 2021. Contains 341941 sequences. (Running on oeis4.)