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

Author

Amiram Eldar, Mar 23 2024

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

Cf. A371418, A371421, A371422.

Similar sequences: A008892, A323328, A361421.

Programs

Mathematica

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

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));}