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#43 by Michael De Vlieger at Fri Mar 10 09:09:55 EST 2023
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#42 by Joerg Arndt at Fri Mar 10 03:37:34 EST 2023
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#41 by Amiram Eldar at Fri Mar 10 03:34:27 EST 2023
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#40 by Amiram Eldar at Fri Mar 10 03:15:06 EST 2023
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| PROG
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(PARI) uhmean(n) = {my(f = factor(n)); n * *prod(i=1, #f~, 2/(1 + +f[i, 1]^f[i, 2])); };
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#39 by Amiram Eldar at Fri Mar 10 03:14:47 EST 2023
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| PROG
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(PARI) uhmean(n) = {my(f = factor(n)); n * prod(i=1, #f~, 2/(1 + f[i, 1]^f[i, 2])); };
lista(kmax) = {my(uh); for(k = 1, kmax, uh = uhmean(k); if(denominator(uh) == 1, print1(uh, ", "))); } \\ Amiram Eldar, Mar 10 2023
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#38 by Amiram Eldar at Fri Mar 10 03:12:55 EST 2023
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| MATHEMATICA
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uh[n_] := n * Times @@ (2/(1 + Power @@@ FactorInteger[n])); uh[1] = 1; Select[Array[uh, 10^6], IntegerQ] (* Amiram Eldar, Mar 10 2023 *)
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#37 by Amiram Eldar at Fri Mar 10 03:11:14 EST 2023
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| PROG
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(PARI) {ud(n)=2^omega(n)} {sud(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))} {H(n)=n*ud(n)/sud(n)} for(n=1, 10000000, if(((n*ud(n))%sud(n))==0, print1(H(n)", "))) - )", "))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
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#36 by Amiram Eldar at Fri Mar 10 03:10:33 EST 2023
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| COMMENTS
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Each term appears a finite number of times in the sequence (Hagis and Lord, 1975). - Amiram Eldar, Mar 10 2023
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| LINKS
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P. Peter Hagis, Jr. and Graham G. Lord, <a href="https://doi.org/10.1090/S0002-9939-1975-0369231-9">Unitary harmonic numbers</a>, Proc. Amer. Math. Soc., 51 (1975), 1-7.
P. Peter Hagis, Jr. and Graham G. Lord, <a href="/A006086/a006086.pdf">Unitary harmonic numbers</a>, Proc. Amer. Math. Soc., 51 (1975), 1-7. (Annotated scanned copy)
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| STATUS
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approved
editing
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#35 by Bruno Berselli at Thu May 30 11:18:55 EDT 2019
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#34 by Michel Marcus at Thu May 30 11:00:13 EDT 2019
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