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

1,1

Comments

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

The larger counterparts are in A380850.

Links

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

Example

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

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]

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(n, ", "))); }

Crossrefs

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

Sequence in context: A046333 A202403 A206618 * A363168 A233430 A220986

Adjacent sequences: A380846 A380847 A380848 * A380850 A380851 A380853

Keyword

nonn,base

Author

Amiram Eldar, Feb 05 2025

Status

approved