A371423 Aliquot-like sequence based on the largest aliquot divisor of the sum of divisors of n (A371418) that starts with 222.

222, 228, 280, 360, 585, 546, 672, 1008, 1612, 1568, 1197, 1040, 1302, 1536, 2046, 2304, 949, 518, 456, 600, 930, 1152, 1105, 756, 1120, 1512, 2400, 3906, 4992, 7140, 12096, 20320, 24192, 40800, 70308, 108416, 135660, 241920, 490560, 902208, 1235456, 1309440, 2354688

Offset

1,1

Comments

222 is the least number k for which the repeated iterations of the mapping k -> A371418(k) seem to generate an unbounded sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1389

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

a(1) = 222 by definition.
a(2) = A371418(a(1)) = A371418(222) = 228.
a(3) = A371418(a(2)) = A371418(228) = 280.

Mathematica

r[n_] := n/FactorInteger[n][[1, 1]]; f[n_] := r[DivisorSigma[1, n]]; NestList[f, 222, 60]

Prog

(PARI) f(n) = {my(s = sigma(n)); if(s == 1, 1, s/factor(s)[1, 1]); }
lista(nmax) = {my(m = 222); for(n = 1, nmax, print1(m, ", "); m = f(m)); }

Crossrefs

Cf. A371418, A371421, A371422.

Similar sequences: A008892, A323328, A361421.

Sequence in context: A078251 A092625 A043612 * A345521 A345775 A361628

Adjacent sequences: A371420 A371421 A371422 * A371424 A371425 A371426

Keyword

nonn

Author

Amiram Eldar, Mar 23 2024

Status

approved