A380850 Greater of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A380845(k) - k is the sum of aliquot divisors of k that have the same binary weight as k.

36068, 145124, 153670, 294075, 290532, 581348, 593100, 1099530, 2066625, 1237830, 2326244, 2338832, 2476870, 6393390, 4652772, 4883976, 6854625, 9279675, 9548325, 6514464, 11725857, 8760548, 9237668, 9305828, 9457356, 8717912, 12190132, 12353716, 10607740, 12493444

Offset: 1

Author

Amiram Eldar, Feb 06 2025

Keywords

• nonn
• base

Comments

Analogous to amicable numbers (A002025 and A002046) with A380845 instead of A000203.

The terms are ordered according to their lesser counterparts (A380849).

Examples

			36068 is a term since A380845(36068) - 36068 = 27940 < 36068 and A380845(27940) - 27940 = 36068.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..12000

Crossrefs

Cf. A000203, A002025, A002046, A380845, A380846, A380849.

Programs

Mathematica

f[n_] := Module[{h = DigitCount[n, 2, 1]}, DivisorSum[n, # &, # < n && DigitCount[#, 2, 1] == h &]];
seq[lim_] := Module[{s = {}, m}, Do[m = f[n]; If[m > n && f[m] == n, AppendTo[s, m]], {n, 1, lim}]; s]; seq[10^6]

PARI

f(n) = {my(h = hammingweight(n)); sumdiv(n, d, d * (d < n && hammingweight(d) == h));}
list(lim) = {my(m); for(n = 1, lim, m = f(n); if(m > n && f(m) == n, print1(m, ", ")));}