A337933 Numbers that are the sum of two abundant numbers in exactly one way.

24, 30, 32, 38, 40, 44, 50, 52, 56, 58, 62, 64, 70, 957, 963, 965, 969, 975, 981, 985, 987, 993, 999, 1001, 1005, 1011, 1015, 1017, 1023, 1025, 1029, 1033, 1035, 1041, 1045, 1047, 1049, 1053, 1057, 1059, 1065, 1071, 1077, 1083, 1085, 1089, 1095, 1101, 1105, 1107, 1113

Offset: 1

Author

Wesley Ivan Hurt, Oct 01 2020

Keywords

• nonn
• fini

Comments

An easy to calculate upper bound for terms is 12*(A047802(2)+1) = 64696932312. This and all larger numbers can be expressed as the sum of an abundant multiple of 6 and a multiple of A047802(2) in at least two ways. - Peter Munn, Feb 09 2021

Examples

			24 is in the sequence since it is the sum of two abundant numbers in exactly one way as 24 = 12 + 12.
30 is in the sequence since it is the sum of two abundant numbers in exactly one way as 30 = 12 + 18.
		

Crossrefs

Cf. A005101, A047802, A048242.

Programs

Mathematica

Table[If[Sum[(1 - Sign[Floor[(2 (n - i))/DivisorSigma[1, n - i]]])*(1 - Sign[Floor[(2 i)/DivisorSigma[1, i]]]), {i, Floor[n/2]}] == 1, n, {}], {n, 1200}] // Flatten