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A335251 Numbers k such that k and k+1 have the same unitary abundance (A129468). 1
1, 20, 35, 143, 208, 2623, 5183, 27796, 11177983, 69677008, 920158207, 1099508482048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Are there any unitary abundant numbers (A034683) in this sequence?

a(12) > 10^11.

a(13) > 8*10^12. Also terms: 2^36 * 68719644673, 2^48 * 281474901625261, 2^64 * 18446632096776339457. - Giovanni Resta, May 29 2020

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

1 is a term since 1 and 2 have the same unitary abundance: A129468(1) = usigma(1) - 2*1 = 1 - 2 = -1, and A129468(2) = usigma(2) - 2*2 = 3 - 4 = -1.

MATHEMATICA

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); udef[n_] := 2*n - usigma[n]; Select[Range[30000], udef[#] == udef[# + 1] &]

CROSSREFS

Cf. A034448, A034683, A129468, A129487, A331412, A335252.

Sequence in context: A048066 A287055 A326403 * A135801 A078210 A174628

Adjacent sequences:  A335248 A335249 A335250 * A335252 A335253 A335254

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, May 28 2020

EXTENSIONS

a(12) from Giovanni Resta, May 29 2020

STATUS

approved

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Last modified September 27 19:04 EDT 2020. Contains 337387 sequences. (Running on oeis4.)