

A109798


Second of a pair of compatible numbers, where two numbers m and n are compatible if sigma(n)2dn=sigma(m)2dm=m+n, for some proper divisors dn and dm of m and n respectively.


2



28, 40, 42, 52, 60, 96, 102, 104, 124, 110, 182, 182, 188, 210, 230, 234, 184, 358, 362, 204, 312, 248, 252, 408, 372, 424, 306, 388, 418, 434, 376, 516, 384, 508, 530, 638, 782, 572, 888, 782, 828, 872, 592, 644, 820, 650, 938, 908, 1026, 1034, 1102, 976, 760
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OFFSET

1,1


COMMENTS

The terms are arranged by the order of their lesser counterparts (A109797).  Amiram Eldar, Oct 26 2019


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000
J. M. Sachs, Admirable Numbers and Compatible Pairs, The Arithmetic Teacher, Vol. 7, No. 6 (1960), pp. 293295.
T. Trotter, Admirable Numbers. [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here.  N. J. A. Sloane, Mar 29 2018]


EXAMPLE

sigma(42)2(1)=962=94 and sigma(52)2(2)=984=94 and 42+52=94 so a(4)=52.


MAPLE

L:=remove(proc(z) isprime(z) end, [$1..10000]): S:=proc(n) map(proc(z) sigma(n) 2*z end, divisors(n) minus {n}) end; CK:=map(proc(z) [z, S(z)] end, L): CL:=[]: for j from 1 to nops(CK)1 do x:=CK[j, 1]; sx:=sigma(x); Sx:=CK[j, 2]; for k from j+1 to nops(CK) while CK[k, 1]<sx do y:=CK[k, 1]; if x+y in Sx intersect CK[k, 2] then CL:=[op(CL), [x, y, x+y]] fi od od;


MATHEMATICA

seq = {}; Do[d = Most[Divisors[n]]; s = Total[d]; Do[m = s  2*d[[k]]; If[m <= 0  m <= n, Continue[]]; delta = DivisorSigma[1, m]  m  n; If[delta > 0 && EvenQ[delta] && delta/2 < m && Divisible[m, delta/2], AppendTo[seq, m]], {k, Length[d], 1, 1}], {n, 1, 750}]; seq (* Amiram Eldar, Oct 26 2019 *)


CROSSREFS

Cf. A109797, A111592.
Sequence in context: A179166 A034964 A195897 * A216594 A324858 A084807
Adjacent sequences: A109795 A109796 A109797 * A109799 A109800 A109801


KEYWORD

nonn


AUTHOR

Walter Kehowski, Aug 15 2005


STATUS

approved



