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A349759 Nobly deficient numbers: numbers k such that both d(k) = A000005(k) and sigma(k) = A000203(k) are deficient numbers (A005100). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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.
LINKS
Jason Earls, Some Smarandache-type sequences and problems concerning abundant and deficient numbers, Smarandache Notions Journal, Vol. 14, No. 1 (2004), pp. 243-250.
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
2 is a term since both d(2) = 2 and sigma(2) = 3 are deficient numbers.
MATHEMATICA
defQ[n_] := DivisorSigma[1, n] < 2*n; nobDefQ[n_] := And @@ defQ /@ DivisorSigma[{0, 1}, n]; Select[Range[400], nobDefQ]
PROG
(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
CROSSREFS
Sequence in context: A023774 A319837 A321699 * A050271 A322742 A307561
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 29 2021
STATUS
approved

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Last modified July 12 21:16 EDT 2024. Contains 374257 sequences. (Running on oeis4.)