A371421 Numbers whose aliquot-like sequence based on the largest aliquot divisor of the sum of divisors of n (A371418) terminates in a fixed point.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 67, 68, 71, 73, 74, 79, 80, 81, 82, 89, 93, 96, 97, 98, 100, 101

Offset

1,2

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..113

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

3 is a term because when we start with 3 and repeatedly apply the mapping x -> A371418(x), we get the sequence 3, 2, 1, 1, 1, ...
40 is a term because when we start with 40 and repeatedly apply the mapping x -> A371418(x), we get the sequence 40, 45, 39, 28, 28, 28, ...

Mathematica

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

Crossrefs

Cf. A371418, A371422, A371423.

A023194 is a subsequence.

Cf. A063769, A080907.

Sequence in context: A008729 A344452 A101373 * A344974 A371022 A107062

Adjacent sequences: A371418 A371419 A371420 * A371422 A371423 A371424

Keyword

nonn

Author

Amiram Eldar, Mar 23 2024

Status

approved