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A306986
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Number of primitive abundant numbers (A071395) < 10^n.
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0
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OFFSET
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1,2
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LINKS
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EXAMPLE
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There are 3 terms of A071395 below 100 (20, 70, and 88), thus a(2) = 3.
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MATHEMATICA
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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 *)
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PROG
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(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); }
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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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