cp's OEIS Frontend

A373047 Least k with exactly n partitions k = x + y + z satisfying sigma*(k) = sigma*(x) + sigma*(y) + sigma*(z), where sigma*(k) is the sum of the anti-divisors of k.

%I A373047 #15 Aug 03 2024 18:58:59
%S A373047 11,33,16,20,26,37,40,19,43,46,93,91,80,76,39,78,155,103,74,135,128,
%T A373047 152,116,117,190,104,187,138,168,147,160,223,208,403,281,173,163,170,
%U A373047 250,243,272,257,258,232,222,278,266,245,352,253,279,256,288,295,231,291
%N A373047 Least k with exactly n partitions k = x + y + z satisfying sigma*(k) = sigma*(x) + sigma*(y) + sigma*(z), where sigma*(k) is the sum of the anti-divisors of k.
%e A373047 a(7) = 40 and 40 has 7 partitions of three numbers, x, y and
%e A373047 z, for which sigma*(65) = sigma*(x) + sigma*(y) + sigma*(z) = 55. In fact:
%e A373047 sigma*(1) + sigma*+(4) + sigma*(35) = 0 + 3 + 52 = 55;
%e A373047 sigma*(1) + sigma*(12) + sigma*(27) = 0 + 13 + 42 = 55;
%e A373047 sigma*(1) + sigma*(14) + sigma*(25) = 0 + 16 + 39 = 55;
%e A373047 sigma*(4) + sigma*(14) + sigma*(22) = 3 + 16 + 36 = 55;
%e A373047 sigma*(5) + sigma*(8) + sigma*(27) = 5 + 8 + 42 = 55;
%e A373047 sigma*(9) + sigma*(13) + sigma*(18) = 8 + 19 + 28 = 55;
%e A373047 sigma*(10) + sigma*(12) + sigma*(18) = 14 + 13 + 28 = 55;
%e A373047 Furthermore 40 is the minimum number to have this property.
%Y A373047 Cf. A066417, A210732, A211223, A211224, A211225, A375154.
%K A373047 nonn,easy
%O A373047 1,1
%A A373047 _Paolo P. Lava_, Aug 02 2024