A364859 Lesser of a pair of S-amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A364858(k).

186, 1184, 2030, 6232, 10744, 66928, 522405, 643336, 5459176, 7677248, 13223490, 16137628, 25596544, 26090325, 28118032, 31772524, 34364912, 40504324, 133178325

Offset

1,1

Comments

S-amicable numbers are analogous to amicable numbers (A002025/A002046) as S-perfect numbers (A118372) are analogous to perfect numbers (A000396).

The greater counterparts are in A364860.

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = A364858(A364860(n)).

Example

186 is a term since A364858(186) = 198 > 186, and A364858(198) = 186.

Mathematica

seq[nmax_] := Module[{s = {1}, sum, sum2, am = {}, ak}, Do[sum = Total[Select[Divisors[n], MemberQ[s, #] &]]; If[sum <= n, AppendTo[s, n]; If[sum < n, sum2 = Total[Select[Most[Divisors[sum]], MemberQ[s, #] &]]; If[sum2 == n, AppendTo[am, sum]]]], {n, 2, nmax}]; am]; seq[10^4]

Prog

(PARI) lista(nmax) = {my(c = 0, s, s2); for(n=2, nmax, s = sumdiv(n, d, !bittest(c, d)*d) - n; if(s > n, c+=1<<n); if(s < n, s2 = sumdiv(s, d, ((d<s)&&!bittest(c, d))*d); if(s2 == n, print1(s, ", ")))); } \\ after M. F. Hasler at A181487

Crossrefs

Cf. A000396, A002025, A002046, A118372, A364858, A364860.

Sequence in context: A286006 A234108 A200199 * A251499 A251492 A289301

Adjacent sequences: A364856 A364857 A364858 * A364860 A364861 A364862

Keyword

nonn,more

Author

Amiram Eldar, Aug 11 2023

Status

approved