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%I #12 Nov 18 2024 02:56:08
%S 72,144,192,216,588,600,648,792,936,992,1056,1224,1302,1320,1560,1736,
%T 1980,2040,2088,2112,2268,2448,2730,2790,2912,3038,3136,3312,3472,
%U 3520,3534,3552,3672,3792,3816,3936,4056,4092,4340,4440,4864,4872,4920,4960
%N Numbers k such that sigma(x) = k has exactly 5 solutions.
%H Amiram Eldar, <a href="/A060661/b060661.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e 72 = sigma(30) = sigma(46) = sigma(51) = sigma(55) = sigma(71).
%t a = Table[ 0, {5000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 5001, a[ [ s ] ]++ ], {n, 1, 5000} ]; Select[ Range[ 5000 ], a[ [ # ] ] == 5 & ]
%t With[{upto=5000},Select[Union[Transpose[Select[Tally[DivisorSigma[ 1, Range[ upto]]],#[[2]]==5&]][[1]]],#<=upto&]] (* _Harvey P. Dale_, Jan 27 2015 *)
%o (PARI) is(k) = invsigmaNum(k) == 5 \\ _Amiram Eldar_, Nov 17 2024, using _Max Alekseyev_'s invphi.gp
%Y Cf. A000203.
%Y Number of solutions: A007369 (0), A007370 (1), A007371 (2), A007372 (3), A060660 (4), this sequence (5), A060662 (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), A060676 (12).
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Apr 18 2001