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%I #18 Feb 12 2020 02:32:52
%S 10,44,184,752,12224,49024,61064,981520,12580864,206158168064,
%T 16492668126208,1080863908958322688,18374686467592175488,
%U 885443715520878608384,4703919738602662723328,226673591177468092350464,232113757366000005450563584,3894222643901120685369075227951104
%N Numbers m such that A076078(m) = m and bigomega(m) >= 2; or in other words, A097214, excluding powers of 2.
%C A076078(m) equals the number of sets of distinct positive integers with a least common multiple of m.
%C If 3*2^k - 1 is an odd prime then 2^k*(3*2^k-1) is in the sequence. - _Farideh Firoozbakht_, May 03 2009
%C For what seems to be an appearance of this sequence in a different context, see Harborth (2013). - _N. J. A. Sloane_, Jun 08 2013
%H F. Firoozbakht, M. F. Hasler, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Hasler/hasler2.html">Variations on Euclid's formula for Perfect Numbers</a>, JIS 13 (2010) #10.3.1.
%H Heiko Harborth, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_41_from57to62.pdf">On h-perfect numbers</a>, Annales Mathematicae et Informaticae, 41 (2013) pp. 57-62.
%e For example, there are 184 sets of distinct positive integers with a least common multiple of 184.
%t f[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu[n/d](2^DivisorSigma[0, d] - 1))]; t = Union[ Table[ f[n], {n, 28000000}]]; Select[t, f[ # ] == # && !IntegerQ[ Log[2, # ]] &] (* _Robert G. Wilson v_, Aug 17 2004 *)
%o (PARI) A076078(n) = {local(f, l, s, t, q); f = factor(n); l = matsize(f)[1]; s = 0; forvec(v = vector(l, i, [0, 1]), q = sum(i = 1, l, v[i]); t = (-1)^(l - q)*2^prod(i = 1, l, f[i, 2] + v[i]); s += t); s; }
%o lista(nn) = {my(w=List([]), m=1, q=2, g); for(k=1, logint(nn, 2)-1, q=nextprime(q+1); m=m*q; for(r=1, nn\2^k-1, g=factor(A076078(m*2^r))[, 2]; if(#g==k+1&&g[2]==1, listput(w, A076078(m*2^r))))); Set(w); } \\ _Jinyuan Wang_, Feb 11 2020
%Y Cf. A097214, A097416, A281993.
%Y Cf. A002235. - _Farideh Firoozbakht_, May 03 2009
%K nonn
%O 1,1
%A _Matthew Vandermast_, Aug 12 2004
%E More terms from _Robert G. Wilson v_, Aug 18 2004
%E More terms from _Jinyuan Wang_, Feb 11 2020
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