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
Keywords
Examples
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.
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.
Programs
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Mathematica
abQ[n_] := DivisorSigma[1, n] > 2*n; nobAbQ[n_] := And @@ abQ /@ DivisorSigma[{0, 1}, n]; Select[Range[500], nobAbQ] -
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
Comments