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A033289 Odd power perfect numbers: numbers k such that opsigma(k) = 2*k, where opsigma(k) = A033634(k). 2
6, 264, 45408, 10177920, 9310826880, 27806077440, 25437179036160, 303753589954560, 277875743791011840, 14504815632384, 13269098919960576, 2534919599177957376, 2318960803647990104064 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If x is OPP and x=2^k*y, gcd(2^k,y)=1, (2^(k+4)+1)/3 is prime, then 4*x*(2^(k+4)+1)/3 is also OPP.

By applying the rule above to a(12) we get that 1772040615644549459607552 is also a term. - Amiram Eldar, Aug 26 2022

LINKS

Table of n, a(n) for n=1..13.

FORMULA

{k: A033634(k) = 2*k}.

MATHEMATICA

f[e_] := If[OddQ[e], e+2, e+1]; fun[p_, e_] := 1 + (p^f[e] - p)/(p^2 - 1); opsigma[1] = 1; opsigma[n_] := Times @@ fun @@@ FactorInteger[n]; Select[Range[50000], opsigma[#] == 2*# &] (* Amiram Eldar, Aug 26 2022 *)

CROSSREFS

Cf. A000978, A033634.

Sequence in context: A316393 A332126 A229579 * A244493 A221900 A229773

Adjacent sequences: A033286 A033287 A033288 * A033290 A033291 A033292

KEYWORD

nonn,more

AUTHOR

Yasutoshi Kohmoto

STATUS

approved

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Last modified February 2 16:10 EST 2023. Contains 360023 sequences. (Running on oeis4.)