

A156942


Odd abundant numbers whose abundance is odd.


5



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
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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.
n 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

R. G. Wilson v, Table of n, a(n) for n = 1..1000


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 && (s2*n)%2 \\ Charles R Greathouse IV, Feb 21 2017


CROSSREFS

Cf. 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



