A380849 Lesser 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.

27940, 112420, 150368, 156840, 225060, 450340, 569376, 925920, 1102200, 1211232, 1802020, 2196592, 2423648, 3377640, 3604260, 4612644, 4874400, 4949160, 5092440, 6375336, 6632808, 6786340, 7155940, 7208740, 7626900, 7685128, 9443060, 9569780, 9643400, 9678020

Offset: 1

Author

Amiram Eldar, Feb 05 2025

Keywords

• nonn
• base

Comments

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

The larger counterparts are in A380850.

Examples

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

Links

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

Crossrefs

Cf. A000203, A002025, A002046, A380845, A380846, A380850.

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, n]], {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(n, ", ")));}