A349759 Nobly deficient numbers: numbers k such that both d(k) = A000005(k) and sigma(k) = A000203(k) are deficient numbers (A005100).

1, 2, 3, 4, 7, 8, 9, 13, 16, 21, 25, 31, 36, 37, 43, 48, 49, 61, 64, 67, 73, 81, 93, 97, 100, 109, 111, 112, 121, 127, 128, 144, 151, 157, 162, 163, 169, 181, 183, 192, 193, 196, 208, 211, 217, 219, 225, 229, 241, 256, 277, 283, 289, 313, 324, 331, 337, 361, 373

Offset: 1

Author

Amiram Eldar, Nov 29 2021

Keywords

• nonn

Comments

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

If p != 5 is a prime such that (p+1)/2 is also a prime (i.e., p is in A005383 \ {5}), then p is a term of this sequence.

Examples

			2 is a term since both d(2) = 2 and sigma(2) = 3 are deficient numbers.
		

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.

Crossrefs

Cf. A000005, A000203, A005100, A005383, A081357, A349758.

Programs

Mathematica

defQ[n_] := DivisorSigma[1, n] < 2*n; nobDefQ[n_] := And @@ defQ /@ DivisorSigma[{0, 1}, n]; Select[Range[400], nobDefQ]

PARI

isdef(k) = sigma(k) < 2*k; \\ A005100
isok(k) = my(f=factor(k)); isdef(numdiv(f)) && isdef(sigma(f)); \\ Michel Marcus, Dec 03 2021