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 A322446 The number of solutions to usigma(k) > esigma(k) below 10^n, where usigma(k) is the sum of unitary divisors of k (A034448) and esigma(k) is the sum of exponential divisors of k (A051377). 0
 5, 74, 776, 7770, 77794, 778337, 7784712, 77833385, 778307928, 7783494530 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The value of the asymptotic density of these solutions was asked in the paper by Trudgian. LINKS Tim Trudgian, The sum of the unitary divisor function, Publications de l'Institut MathÃ©matique (Beograd), Vol. 97, No. 111 (2015), pp. 175-180. FORMULA Lim_{n->oo} a(n)/10^n = 0.778... EXAMPLE Below 10^1 there are 5 numbers k with usigma(k) > esigma(k): 2, 3, 5, 6, and 7. Thus a(1) = 5. MATHEMATICA aQ[1] = False; fun[p_, e_] := DivisorSum[e, p^# &]; aQ[n_] := Times @@ (1 + Power @@@ (f = FactorInteger[n])) > Times @@ (fun @@@ f); c = 0; k = 1; s = {}; Do[While[k < 10^n, If[aQ[k], c++]; k++]; AppendTo[s, c], {n, 1, 6}]; s CROSSREFS Cf. A034448, A051377, A236474. Sequence in context: A051156 A092826 A334258 * A065894 A233013 A126740 Adjacent sequences:  A322443 A322444 A322445 * A322447 A322448 A322449 KEYWORD nonn,more AUTHOR Amiram Eldar, Aug 28 2019 STATUS approved

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Last modified May 15 13:52 EDT 2021. Contains 343920 sequences. (Running on oeis4.)