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 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 (list; graph; refs; listen; history; text; internal format)
 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. 42-67, Ed. H. D. Ruderman, Mu Alpha Theta OK 1978. LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..10000 Charles Robert Wall, Topics related to the sum of unitary divisors of an integer, Ph.D. diss., University of Tennessee, 1970. MAPLE isA034683 := proc(n) is(A034448(n) > 2*n) ; end proc: for n from 1 do if isA034683(n) then print(n); end if; end do: # R. J. Mathar, Nov 10 2014 MATHEMATICA usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; Select[Range[1000], usigma[#] > 2#&] (* Jean-François Alcover, Mar 23 2020, after Giovanni Resta in A034448 *) 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 Subsequence of A005101. Cf. A034444, A034448, A129487, A302993. Sequence in context: A053858 A075819 A306217 * A328328 A302574 A087248 Adjacent sequences: A034680 A034681 A034682 * A034684 A034685 A034686 KEYWORD nonn,changed AUTHOR Erich Friedman STATUS approved

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Last modified April 23 07:42 EDT 2024. Contains 371905 sequences. (Running on oeis4.)