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 A091321 OU-Sigma multiperfect numbers. 4
 1, 6, 28, 90, 120, 496, 672, 8128, 10080, 63700, 220500, 523776, 1323000, 1528800, 2056320, 7856640, 33550336, 44553600, 162729000, 252927360, 459818240, 1379454720, 1476304896, 1980840960, 8589869056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The OU-Sigma function is defined as OU-Sigma(n) = A107749(n). Then an OU-Sigma perfect number satisfies OU-Sigma(n) = k*n for some k. Every perfect number is here because OE-Sigma(2^(m-1)*M_m) = Sigma(2^(m-1))*UnitarySigma(M_m) = Sigma(2^(m-1))*Sigma(M_m) = 2^m*M_m. Also in the sequence are 33550336, 8589869056, 22144573440, 51001180160, 153003540480, 243643438080, 583125903360, 71724486113280, 1555825650042470400, but there may be missing terms in between. LINKS EXAMPLE Sequence begins 2*3, 2*3^2*5, 2^2*7, 2^2*5^2*7^2*13, 2^3*3*5, 2^4*31, 2^5*3^2*5*7, ... MATHEMATICA fun[p_, e_] := If[p==2, 2^(e+1)-1, p^e+1]; f[n_] := If[n==1, 1, Times @@ fun @@@ FactorInteger[n]]; aQ[n_] := Divisible[f[n], n]; Select[Range[65000], aQ] (* Amiram Eldar, Mar 17 2019 *) PROG (PARI) f(n)= my(fm=factor(n)); prod(k=1, matsize(fm)[1], if(fm[k, 1]==2, 2^(fm[k, 2]+1)-1, fm[k, 1]^fm[k, 2]+1)); \\ A107749 isok(n) = (f(n) % n) == 0; \\ Michel Marcus, Jan 24 2019 CROSSREFS Cf. A107749, A091322. Sequence in context: A302650 A055711 A141255 * A125310 A336535 A342380 Adjacent sequences:  A091318 A091319 A091320 * A091322 A091323 A091324 KEYWORD nonn,more AUTHOR Yasutoshi Kohmoto, Feb 17 2004 EXTENSIONS Terms 220500 to 2056320 by R. J. Mathar, Jun 02 2011 Corrected and extended by Michel Marcus, Jan 24 2019 a(19)-a(25) from Amiram Eldar, Mar 17 2019 STATUS approved

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Last modified April 12 11:51 EDT 2021. Contains 342920 sequences. (Running on oeis4.)