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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 (list; graph; refs; listen; history; text; internal format)
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. 293-295.

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)=96-2=94 and sigma(52)-2(2)=98-4=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

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Last modified March 31 20:55 EDT 2020. Contains 333151 sequences. (Running on oeis4.)