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A331371 Numbers k such that k and k+1 are both half-Zumkeller numbers (A246198). 0
224, 440, 1224, 2024, 3968, 5624, 11024, 18224, 35720, 38024, 50624, 53360, 65024, 74528, 81224, 140624, 148224, 159200, 164024, 184040, 189224, 194480, 207024, 216224, 233288, 245024, 314720, 354024, 370880, 378224, 416024, 423800, 442224, 455624, 497024, 511224 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

224 is a term since both 224 and 225 are half-Zumkeller numbers: the proper divisors of 224 are {1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112} and 1 + 2 + 4 + 7 + 8 + 14 + 16 + 32 + 56 = 28 + 112, and the proper divisors of 225 are {1, 3, 5, 9, 15, 25, 45, 75} and 1 + 3 + 15 + 25 + 45 = 5 + 9 + 75.

MATHEMATICA

hzQ[n_] := Module[{d = Most @ Divisors[n], sum, x}, sum = Plus @@ d; EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]; hzq1 = False; s = {}; Do[hzq2 = hzQ[n]; If[hzq1 && hzq2, AppendTo[s, n - 1]]; hzq1 = hzq2, {n, 2, 6000}]; s

CROSSREFS

Cf. A246198, A246199, A328327.

Sequence in context: A240529 A177770 A202442 * A094209 A158227 A061524

Adjacent sequences:  A331368 A331369 A331370 * A331372 A331373 A331374

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 03 2020

STATUS

approved

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Last modified September 26 12:04 EDT 2021. Contains 347665 sequences. (Running on oeis4.)