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%I #16 Feb 22 2019 02:07:03
%S 1,28,29,62,84,182,230,252,344,756,944,2268,6710,6804,20264,20412,
%T 36224,61236,183708,538112,551124,1653372,2085710,4960116,14503550,
%U 14880348,33665024,44641044,55328384,133923132,134438912,401769396,615206030,1082574464
%N Numbers n such that (A000203(n)+28)/n is an integer.
%C Contains the subset of all n of the form 28*3^k.
%C Generalized sequences are defined by A*A000203(n)+ B = C*n with A,B,C integers.
%C Then we get for different settings of A, B, C hyperperfect numbers:
%C A=1, C=2, B=0 gives A000396. A=1, C=2, B=1 gives A000079.
%C A=1, C=2, B=2 gives A056006. A=1, C=2, B=4 gives A125246. A=1, C=2, B=6 gives A141548.
%C A=1, C=2, B=8 gives A125247. A=1, C=2, B=10 gives A101223. A=1, C=2, B=12 gives A141549.
%C A=1, C=2, B=14 gives A141550. A=1, C=2, B=16 gives A125248. A=1, C=2, B=0 gives A000396.
%C A=1, C=2, B=0 gives A000396. A=1, C=3, B=0 gives A005820.
%C Not in the OEIS: A=1, C=3, B=12,18,28,... A=2, C=3, B=21,27,33,45,... A=3, C=4, B=20,...
%C Terms not of the form 28*3^n: 1, 29, 62, 182, 230, 344, 944, 6710, 20264, 36224, 538112, 2085710, 14503550, 33665024, 55328384, ..., . [_Robert G. Wilson v_, Sep 05 2010]
%H Graeme L. Cohen, Herman J. J. te Riele, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.868">Iterating the Sum-of-Divisors Function</a>, Experimental Mathematics, Vol.5 (1996), No. 2, pp.91-100.
%p A000203 := proc(n) numtheory[sigma](n) ; end proc:
%p isA152302 := proc(n) (A000203(n)+28) mod n = 0 ; end proc:
%p for n from 1 to 1000000 do if isA152302(n) then printf("%d,",n) ; end if ; end do: # _R. J. Mathar_, Aug 25 2010
%t fQ[n_] := Divisible[ DivisorSigma[1, n] + 28, n]; lst = {}; k = 1; While[k < 10^9/4, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst (* _Robert G. Wilson v_, Sep 05 2010 *)
%Y Cf. A000203, A000396, A000079, A005820, A056006, A125246, A141548, A125247, A101223, A141549, A141550, A125248,
%K nonn
%O 1,2
%A _Ctibor O. Zizka_, Jun 30 2009
%E Missing terms (1, 29, 182,..) inserted, 7 terms added, comment corrected - _R. J. Mathar_, Aug 25 2010
%E a(22)-a(30) from _Robert G. Wilson v_, Sep 05 2010
%E a(31)-a(34) from _Donovan Johnson_, Nov 03 2011
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