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Numbers k such that k and k+2 have the same unitary abundance (A129468).
2

%I #12 May 30 2020 11:18:46

%S 12,63,117,323,442,1073,1323,1517,3869,5427,6497,12317,18419,35657,

%T 69647,79919,126869,133787,151979,154007,163332,181427,184619,333797,

%U 404471,439097,485237,581129,621497,825497,1410119,2696807,3077909,3751619,5145341,6220607

%N Numbers k such that k and k+2 have the same unitary abundance (A129468).

%C Are 12, 442 and 163332 the only even terms?

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

%C No further even terms up to 10^13. - _Giovanni Resta_, May 30 2020

%H Amiram Eldar, <a href="/A335252/b335252.txt">Table of n, a(n) for n = 1..300</a>

%e 12 is a term since 12 and 14 have the same unitary abundance: A129468(12) = usigma(12) - 2*12 = 20 - 24 = -4, and A129468(14) = usigma(14) - 2*14 = 24 - 28 = -4.

%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); udef[n_] := 2*n - usigma[n]; Select[Range[10^5], udef[#] == udef[# + 2] &]

%Y The unitary version of A330901.

%Y Cf. A034448, A034683, A129468, A129487, A335251.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 28 2020