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A306986 Number of primitive abundant numbers (A071395) < 10^n.

%I A306986 #12 Mar 26 2023 02:22:21
%S A306986 0,3,14,98,441,1734,8667,41653,213087,1123424
%N A306986 Number of primitive abundant numbers (A071395) < 10^n.
%H A306986 Michael R. Avidon, <a href="https://eudml.org/doc/206918">On the distribution of primitive abundant numbers</a>, Acta Arithmetica, Vol. 77, No. 2 (1996), pp. 195-205.
%H A306986 Paul Erdős, <a href="https://doi.org/10.1112/jlms/s1-10.37.49">On primitive abundant numbers</a>, J. London Math. Soc., Volume s1-10, Issue 1 (1935), pp. 49-58, <a href="https://users.renyi.hu/~p_erdos/1935-05.pdf">alternative link</a>.
%H A306986 Aleksandar Ivić, <a href="http://real-j.mtak.hu/5462/1/StudScientMath_20.pdf#page=189">The distribution of primitive abundant numbers</a>, Studia Sci. Math. Hungar., Vol. 20 (1985), pp. 183-187.
%e A306986 There are 3 terms of A071395 below 100 (20, 70, and 88), thus a(2) = 3.
%t A306986 paQ[n_] := DivisorSigma[1, n] > 2n && Times @@ Boole@ Map[DivisorSigma[1, #] < 2 # &, Most@ Divisors@ n] == 1;  c = 0; k = 1;  seq={}; Do[ While[ k < 10^n, If[ paQ[k], c++ ]; k ++]; AppendTo[seq, c], {n, 1, 5}]; seq (* after _Michael De Vlieger_ at A071395 *)
%o A306986 (PARI) ispab(n) = {my(f = factor(n), r, p, e); r = sigma(f, -1); if(r <= 2, return(0)); if(vecmax(vector(#f~, i, p = f[i, 1]; e = f[i, 2]; (p^(e + 1) - p)/(p^(e + 1) - 1))) * r < 2, 1, 0);}
%o A306986 lista(nmax) = {my(c = 0, r = 10); for(k = 1, 10^nmax, if(ispab(k), c++); if(k+1 == r, print1(c, ", "); r *= 10));} \\ _Amiram Eldar_, Mar 26 2023
%Y A306986 Cf. A071395, A302992.
%K A306986 nonn,more
%O A306986 1,2
%A A306986 _Amiram Eldar_, Mar 18 2019
%E A306986 a(10) from _Amiram Eldar_, Mar 26 2023