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

1,1

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

Links

Table of n, a(n) for n=1..51.

Example

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.

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

Crossrefs

Cf. A005101, A047802, A048242.

Sequence in context: A048260 A333946 A354809 * A114635 A077969 A122181

Adjacent sequences: A337930 A337931 A337932 * A337934 A337935 A337936

Keyword

nonn,fini

Author

Wesley Ivan Hurt, Oct 01 2020

Status

approved