A371420 - OEIS

%I #6 Mar 23 2024 08:23:16

%S 14,62,124,189,254,508,2032,16382,32764,131056,262142,524284,524224,

%T 1048574,2097148,2097136,8388592,8388544,33554368,536866816,

%U 2147479552,4294967294,8589934588,34359738352,34359672832,137438953408

%N 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).

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

%H Robert D. Carmichael, <a href="https://doi.org/10.5951/MT.14.6.0305">Empirical Results in the Theory of Numbers</a>, The Mathematics Teacher, Vol. 14, No. 6 (1921), pp. 305-310; <a href="https://www.jstor.org/stable/27950349">alternative link</a>. See p. 309.

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

%t 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

%o (PARI) f(n) = {my(s = sigma(n)); if(s == 1, 1, s/factor(s)[1, 1]);}

%o lista(nmax) = {my(m); for(n = 1, nmax, m = f(n); if(m > n && f(m) == n, print1(m, ", ")));}

%Y Cf. A371418, A371419.

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

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Mar 23 2024