A371420 Greater member of Carmichael's variant of amicable pair: numbers k < m such that s(k) = m and s(m) = k, where s(k) = A371418(k).

14, 62, 124, 189, 254, 508, 2032, 16382, 32764, 131056, 262142, 524284, 524224, 1048574, 2097148, 2097136, 8388592, 8388544, 33554368, 536866816, 2147479552, 4294967294, 8589934588, 34359738352, 34359672832, 137438953408

Offset

1,1

Comments

The terms are ordered according to their lesser counterparts (A371419).

Links

Table of n, a(n) for n=1..26.

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

14 is a term since A371418(14) = 12 < 14, and A371418(12) = 14.

Mathematica

r[n_] := n/FactorInteger[n][[1, 1]]; s[n_] := r[DivisorSigma[1, n]]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 1, 10^6}]; seq

Prog

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

Crossrefs

Cf. A371418, A371419.

Similar sequences: A002046, A002953, A126166, A126170, A259039, A292981, A322542, A324709, A348344.

Sequence in context: A189948 A252255 A025415 * A307253 A125849 A003695

Adjacent sequences: A371417 A371418 A371419 * A371421 A371422 A371423

Keyword

nonn,more

Author

Amiram Eldar, Mar 23 2024

Status

approved