A349758 Nobly abundant numbers: numbers k such that both d(k) = A000005(k) and sigma(k) = A000203(k) are abundant numbers (A005101).

60, 84, 90, 96, 108, 126, 132, 140, 150, 156, 160, 180, 198, 204, 220, 224, 228, 234, 240, 252, 260, 276, 294, 300, 306, 308, 315, 336, 340, 342, 348, 350, 352, 360, 364, 372, 380, 396, 414, 416, 420, 432, 444, 460, 476, 480, 486, 490, 492, 495, 500, 504, 516

Offset

1,1

Comments

Analogous to sublime numbers (A081357), with abundant numbers instead of perfect numbers.

The least odd term is a(27) = 315 and the least term that is coprime to 6 is a(298) = 1925.

References

József Sándor and E. Egri, Arithmetical functions in algebra, geometry and analysis, Advanced Studies in Contemporary Mathematics, Vol. 14, No. 2 (2007), pp. 163-213.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Jason Earls, Some Smarandache-type sequences and problems concerning abundant and deficient numbers, Smarandache Notions Journal, Vol. 14, No. 1 (2004), pp. 243-250.

József Sándor, Selected Chapters of Geometry, Analysis and Number Theory, 2005, pp. 132-134.

Shikha Yadav and Surendra Yadav, Multiplicatively perfect and related numbers, Journal of Rajasthan Academy of Physical Sciences, Vol. 15, No. 4 (2016), pp. 345-350.

Example

60 is a term since both d(60) = 12 and sigma(60) = 168 are abundant numbers: sigma(12) = 28 > 2*12 = 24 and sigma(168) = 480 > 2*168 = 336.

Mathematica

abQ[n_] := DivisorSigma[1, n] > 2*n; nobAbQ[n_] := And @@ abQ /@ DivisorSigma[{0, 1}, n]; Select[Range[500], nobAbQ]

Prog

(PARI) isab(k) = sigma(k) > 2*k; \\ A005101
isok(k) = my(f=factor(k)); isab(numdiv(f)) && isab(sigma(f)); \\ Michel Marcus, Dec 02 2021

Crossrefs

Cf. A000005, A000203, A005101, A081357, A349759.

A349760 is a subsequence.

Sequence in context: A323979 A067207 A261375 * A217740 A123712 A178212

Adjacent sequences: A349755 A349756 A349757 * A349759 A349760 A349761

Keyword

nonn

Author

Amiram Eldar, Nov 29 2021

Status

approved