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

Author

Amiram Eldar, Mar 23 2024

Keywords

• nonn

Comments

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

Examples

			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, ...
		

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.

Crossrefs

Cf. A371418, A371421, A371423.

Similar sequences: A127655, A127660, A127665.

Programs

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]