A380850 -id:A380850 - cp's OEIS frontend

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

Amiram Eldar, Feb 05 2025

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

The larger counterparts are in A380850.

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

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

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

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]

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, ", ")));}

A383366 Smallest of a sociable triple i < j < k such that j = s(i), k = s(j), and i = s(k), where s(k) = A380845(k) - k is the sum of aliquot divisors of k that have the same binary weight as k.

Original entry on oeis.org

4400700, 12963816, 29878920, 38353800, 44973480, 51894304, 52208520, 67849656, 73134432, 81685080, 100711656, 103759848, 105096096, 113044896, 113161320, 114608032, 128639034, 135465912, 135559080, 136786200, 139242740, 148758120, 156686088, 159628350, 171090416

Offset: 1

Amiram Eldar, Apr 24 2025

			4400700 is a term since s(4400700) = 4840770, s(4840770) = 5456868, and s(5456868) = 4400700.

Amiram Eldar, Table of n, a(n) for n = 1..4400
Amiram Eldar, Table of n, a(n), s(a(n)), s(s(a(n))) for n = 1..4400.

Cf. A380845, A380846, A380849, A380850.

f[n_] := Module[{h = DigitCount[n, 2, 1]}, DivisorSum[n, # &, # < n && DigitCount[#, 2, 1] == h &]]; q[k_] := Module[{k1 = f[k], k2}, If[k1 <= k, False, k2 = f[k1]; k2 > k && f[k2] == k]]; Select[Range[13000000], q]

f(n) = {my(h = hammingweight(n)); sumdiv(n, d, d * (d < n && hammingweight(d) == h)); }
isok(k) = {my(k1 = f(k), k2); if(k1 <= k, 0, k2 = f(k1); k2 > k && f(k2) == k);}

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI