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

1,1

Comments

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

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

Links

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

Example

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

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]

Prog

(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, ", "))); }

Crossrefs

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

Sequence in context: A031827 A097694 A209956 * A256365 A011766 A138556

Adjacent sequences: A380847 A380848 A380849 * A380851 A380853 A380854

Keyword

nonn,base

Author

Amiram Eldar, Feb 06 2025

Status

approved