

A034683


Unitary abundant numbers: numbers k such that usigma(k) > 2*k.


38



30, 42, 66, 70, 78, 102, 114, 138, 150, 174, 186, 210, 222, 246, 258, 282, 294, 318, 330, 354, 366, 390, 402, 420, 426, 438, 462, 474, 498, 510, 534, 546, 570, 582, 606, 618, 630, 642, 654, 660, 678, 690, 714, 726, 750, 762, 770, 780, 786, 798, 822, 834
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OFFSET

1,1


COMMENTS

If a term n in the sequence ends in neither 0 nor 5, then 10*n is also in the sequence.  Lekraj Beedassy, Jun 11 2004
The lower asymptotic density of this sequence is larger than 1/18 = 0.0555... which is the density of its subsequence of numbers of the form 6*m where gcd(m, 6) = 1 and m > 1. Numerically, based on counts of terms below 10^n (A302993), it seems that this sequence has an asymptotic density which equals to about 0.070034...  Amiram Eldar, Feb 13 2021
The asymptotic density of this sequence is in the interval (0.0674, 0.1055) (Wall, 1970).  Amiram Eldar, Apr 18 2024


REFERENCES

C. Sung, Mathematical Buds, "Unitary Divisors", Chap. V pp. 4267, Ed. H. D. Ruderman, Mu Alpha Theta OK 1978.


LINKS



MAPLE

isA034683 := proc(n)
end proc:
for n from 1 do
if isA034683(n) then
print(n);
end if;


MATHEMATICA

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];


PROG

(PARI) is(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]) > 2*n; } \\ Amiram Eldar, Apr 18 2024


CROSSREFS



KEYWORD

nonn,changed


AUTHOR



STATUS

approved



