A371422 Numbers whose aliquot-like sequence based on the largest aliquot divisor of the sum of divisors of n (A371418) terminates in a cycle of length 2.

12, 14, 15, 23, 29, 42, 44, 48, 54, 56, 60, 62, 65, 66, 69, 70, 72, 75, 76, 77, 78, 83, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95, 99, 102, 107, 108, 110, 111, 112, 114, 115, 117, 118, 119, 120, 123, 124, 125, 128, 129, 131, 132, 134, 135, 136, 137, 139, 140, 142

Offset

1,1

Comments

It is unknown whether 222 is a term of this sequence or not (see A371423).

Links

Amiram Eldar, Table of n, a(n) for n = 1..108

Robert D. Carmichael, Empirical Results in the Theory of Numbers, The Mathematics Teacher, Vol. 14, No. 6 (1921), pp. 305-310; alternative link. See p. 309.

Example

12 is a term because when we start with 12 and repeatedly apply the mapping x -> A371418(x), we get the sequence 12, 14, 12, 14, ...
76 is a term because when we start with 76 and repeatedly apply the mapping x -> A371418(x), we get the sequence 76, 70, 72, 65, 42, 48, 62, 48, 62, ...

Mathematica

r[n_] := n/FactorInteger[n][[1, 1]]; f[n_] := r[DivisorSigma[1, n]];
q[n_] := Module[{m = NestWhileList[f, n, UnsameQ, All][[-1]], k}, k = f[m]; k != m && f[k] == m]; Select[Range[221], q]

Crossrefs

Cf. A371418, A371421, A371423.

Similar sequences: A127655, A127660, A127665.

Sequence in context: A344980 A344883 A290001 * A080693 A135739 A096923

Adjacent sequences: A371419 A371420 A371421 * A371423 A371424 A371425

Keyword

nonn

Author

Amiram Eldar, Mar 23 2024

Status

approved