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A060665 Numbers k such that sigma(x) = k has exactly 9 solutions.

%I A060665 #13 Nov 18 2024 02:55:53
%S A060665 360,480,1488,1800,1824,2184,2232,2640,3120,3420,3696,3744,3960,4200,
%T A060665 5292,5580,5808,6144,7344,7980,8100,8352,8448,8784,9144,10164,10296,
%U A060665 11592,11664,11970,12432,13968,14520,14560,15504,15600,15912,16224
%N A060665 Numbers k such that sigma(x) = k has exactly 9 solutions.
%C A060665 Do we have a(n) ~ c*n where c ~= 700? - _David A. Corneth_, Sep 23 2019
%H A060665 David A. Corneth, <a href="/A060665/b060665.txt">Table of n, a(n) for n = 1..10046</a> (first 8577 terms from Robert Israel, terms <= 7*10^6)
%H A060665 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e A060665 360 = sigma(120) = sigma(174) = sigma(184) = sigma(190) = sigma(267) = sigma(295) = sigma(319) = sigma(323) = sigma(359).
%p A060665 N:= 60000: # to get terms <= N
%p A060665 V:= Vector(N):
%p A060665 for k from 1 to N-1 do
%p A060665   t:= numtheory:-sigma(k);
%p A060665   if t <= N then V[t]:= V[t]+1 fi
%p A060665 od:
%p A060665 select(t -> V[t]=9, [$1..N]); # _Robert Israel_, Sep 22 2019
%t A060665 a = Table[ 0, {20000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 20001, a[ [ s ] ]++ ], {n, 1, 20000} ]; Select[ Range[ 20000 ], a[ [ # ] ] == 9 & ]
%o A060665 (PARI) upto(n) = {my(v = vecsort(vector(n, i, sigma(i))), res = List()); for(i = 2, #v - 9, if(v[i-1] <= n && v[i-1] != v[i] && v[i] == v[i + 8] && v[i] != v[i+9], listput(res, v[i]))); res} \\ _David A. Corneth_, Sep 23 2019
%o A060665 (PARI) is(k) = invsigmaNum(k) == 9 \\ _Amiram Eldar_, Nov 18 2024, using _Max Alekseyev_'s invphi.gp
%Y A060665 Cf. A000203.
%Y A060665 Number of solutions: A007369 (0), A007370 (1), A007371 (2), A007372 (3), A060660 (4), A060661 (5), A060662 (6), A060663 (7), A060664 (8), this sequence (9), A060666 (10), A060678 (11), A060676 (12).
%K A060665 nonn
%O A060665 1,1
%A A060665 _Robert G. Wilson v_, Apr 18 2001