A162302 Numbers n such that (A000203(n)+28)/n is an integer.

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

Offset: 1

Author

Ctibor O. Zizka, Jun 30 2009

Keywords

• nonn

Comments

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 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,...

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]

Links

• Graeme L. Cohen, Herman J. J. te Riele, Iterating the Sum-of-Divisors Function, Experimental Mathematics, Vol.5 (1996), No. 2, pp.91-100.

Crossrefs

Cf. A000203, A000396, A000079, A005820, A056006, A125246, A141548, A125247, A101223, A141549, A141550, A125248,

Programs

Maple

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

Mathematica

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 *)

Extensions

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