A371952 -id:A371952 - cp's OEIS frontend

A371953 Weird numbers whose abundance is a weird number with weird abundance (A371952).

13516958630, 13662237610, 14483820470, 16161187910, 16266406870, 17187072770, 17779204310, 18055129190, 19265719130, 20027984690, 20291032090, 20945054548, 21036318170, 21395831170, 21983936030, 22134086030, 22335605390, 23837897510, 24709171970, 25630894310, 26286582910

Offset: 1

Amiram Eldar, Apr 14 2024

nonn

Terms k of A006037 such that A033880(k) and A033880(A033880(k)) are also terms of A006037.

Are there numbers k such that k, A033880(k), A033880(A033880(k)), and A033880(A033880(A033880(k))) are all terms of A006037? There are none below 10^11.

			13516958630 is a term because it is a weird number, A033880(13516958630) = sigma(13516958630) - 2*13516958630 = 833308916 is a weird number, and A033880(833308916) = sigma(833308916) - 2*833308916 = 7975928 is also a weird number.

Amiram Eldar, Table of n, a(n) for n = 1..146 (terms below 10^11)
Wikipedia, Weird number.

Subsequence of A006037, A371920 and A371952.

Cf. A000203 (sigma), A033880 (abundance).

A371950 Weird numbers (A006037) whose sum of aliquot divisors is also a weird number.

Original entry on oeis.org

97930, 132230, 146930, 191030, 205730, 215530, 244930, 259630, 279230, 308630, 362530, 411530, 440930, 524230, 529130, 583030, 597730, 602630, 632030, 646730, 705530, 730030, 808430, 891730, 921130, 955430, 970130, 1014230, 1024030, 1028930, 1102430, 1215130, 1435630

Offset: 1

Amiram Eldar, Apr 14 2024

nonn

Terms k of A006037 such that A001065(k) is also a term of A006037.

			97930 is a term because it is a weird number, and A001065(97930) = sigma(97930) - 97930 = 103670 is also a weird number.

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

Subsequence of A006037 and A125639.

Cf. A000203 (sigma), A001065, A371951, A371952.

With[{weirds = Import["https://oeis.org/a006037/b006037.txt", "Table"][[;; , 2]]}, Select[weirds, (s = DivisorSigma[1, #] - #) <= Last[weirds] && MemberQ[weirds, s] &]]

cp's OEIS Frontend

A371953 Weird numbers whose abundance is a weird number with weird abundance (A371952).

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