A156942 Odd abundant numbers whose abundance is odd.

11025, 99225, 245025, 275625, 342225, 540225, 893025, 1334025, 1863225, 2205225, 2480625, 3080025, 3186225, 3980025, 4601025, 4862025, 5832225, 6125625, 6890625, 7868025, 8037225, 8555625, 9272025, 9828225, 10595025, 10989225

Offset

1,1

Comments

Number of terms <10^n: 0, 0, 0, 0, 2, 7, 24, 83, 250, 792, 2484, 7988, 25383, 80082, ..., . Not all are a multiple of 25, i.e.; 81162081 = 9009^2 = (9*7*11*13)^2. See A156943.

Any term must be an odd square. Square roots are in A174830.

Indeed, the sum of divisors of any number isn't odd unless it's a square or twice a square (A028982), and to get the abundance, twice the number is subtracted, so the parity remains the same. - M. F. Hasler, Jan 26 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from R. G. Wilson v)

Formula

a(n) = A174830(n)^2. - M. F. Hasler, Jan 26 2020

Mathematica

fQ[n_] := Block[{ds = DivisorSigma[1, n] - 2 n}, ds > 0 && OddQ@ ds]; Select[ Range[1, 12006223, 2], fQ @# &]

Prog

(PARI) is(n)=my(s=sigma(n)); n%2 && s>2*n && (s-2*n)%2 \\ Charles R Greathouse IV, Feb 21 2017

Crossrefs

Cf. A028982, A033880, A156903, A156943, A174830.

Sequence in context: A160711 A129087 A239828 * A325311 A164518 A198208

Adjacent sequences: A156939 A156940 A156941 * A156943 A156944 A156945

Keyword

nonn

Author

Robert G. Wilson v, Feb 18 2009

Extensions

Edited by Robert G. Wilson v at the suggestion of T. D. Noe, Mar 30 2010

Status

approved