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A162302
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Numbers n such that (A000203(n)+28)/n is an integer.
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0
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1, 28, 29, 62, 84, 182, 230, 252, 344, 756, 944, 2268, 6710, 6804, 20264, 20412, 36224, 61236, 183708, 538112, 551124, 1653372, 2085710, 4960116, 14503550, 14880348, 33665024, 44641044, 55328384, 133923132, 134438912, 401769396, 615206030, 1082574464
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OFFSET
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1,2
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COMMENTS
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Contains the subset of all n of the form 28*3^k.
Generalized sequences are defined by A*A000203(n)+ B = C*n with A,B,C integers.
Then we get for different settings of A, B, C hyperperfect numbers:
A=1, C=2, B=0 gives A000396. A=1, C=2, B=1 gives A000079.
A=1, C=2, B=2 gives A056006. A=1, C=2, B=4 gives A125246. A=1, C=2, B=6 gives A141548.
A=1, C=2, B=8 gives A125247. A=1, C=2, B=10 gives A101223. A=1, C=2, B=12 gives A141549.
A=1, C=2, B=14 gives A141550. A=1, C=2, B=16 gives A125248. A=1, C=2, B=0 gives A000396.
A=1, C=2, B=0 gives A000396. A=1, C=3, B=0 gives A005820.
Not in OEIS : A=1, C=3, B=12,18,28,... A=2, C=3, B=21,27,33,45,... A=3, C=4, B=20,...
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]
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LINKS
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Table of n, a(n) for n=1..34.
Graeme L. Cohen, Herman J. J. te Riele, Iterating the Sum-of-Divisors Function, Experimental Mathematics, Vol.5 (1996), No. 2, pp.91-100.
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MAPLE
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A000203 := proc(n) numtheory[sigma](n) ; end proc:
isA152302 := proc(n) (A000203(n)+28) mod n = 0 ; end proc:
for n from 1 to 1000000 do if isA152302(n) then printf("%d, ", n) ; end if ; end do: # R. J. Mathar, Aug 25 2010
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A000203, A000396, A000079, A005820, A056006, A125246, A141548, A125247, A101223, A141549, A141550, A125248,
Sequence in context: A042572 A042570 A042568 * A042592 A042594 A042590
Adjacent sequences: A162299 A162300 A162301 * A162303 A162304 A162305
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KEYWORD
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nonn
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AUTHOR
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Ctibor O. Zizka, Jun 30 2009
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EXTENSIONS
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Missing terms (1, 29, 182,..) inserted, 7 terms added, comment corrected - R. J. Mathar, Aug 25 2010
a(22)-a(30) from Robert G. Wilson v, Sep 05 2010
a(31)-a(34) from Donovan Johnson, Nov 03 2011
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STATUS
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approved
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