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 A097215 Numbers m such that A076078(m) = m and bigomega(m) >= 2; or in other words, A097214, excluding powers of 2. 3
 10, 44, 184, 752, 12224, 49024, 61064, 981520, 12580864, 206158168064, 16492668126208, 1080863908958322688, 18374686467592175488, 885443715520878608384, 4703919738602662723328, 226673591177468092350464, 232113757366000005450563584, 3894222643901120685369075227951104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A076078(m) equals the number of sets of distinct positive integers with a least common multiple of m. 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 For what seems to be an appearance of this sequence in a different context, see Harborth (2013). - N. J. A. Sloane, Jun 08 2013 LINKS F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1. Heiko Harborth, On h-perfect numbers, Annales Mathematicae et Informaticae, 41 (2013) pp. 57-62. EXAMPLE For example, there are 184 sets of distinct positive integers with a least common multiple of 184. MATHEMATICA 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 *) PROG (PARI) A076078(n) = {local(f, l, s, t, q); f = factor(n); l = matsize(f); 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; } 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==1, listput(w, A076078(m*2^r))))); Set(w); } \\ Jinyuan Wang, Feb 11 2020 CROSSREFS Cf. A097214, A097416, A281993. Cf. A002235. - Farideh Firoozbakht, May 03 2009 Sequence in context: A220994 A097416 A076373 * A281993 A126397 A164607 Adjacent sequences:  A097212 A097213 A097214 * A097216 A097217 A097218 KEYWORD nonn AUTHOR Matthew Vandermast, Aug 12 2004 EXTENSIONS More terms from Robert G. Wilson v, Aug 18 2004 More terms from Jinyuan Wang, Feb 11 2020 STATUS approved

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Last modified October 30 16:01 EDT 2020. Contains 338081 sequences. (Running on oeis4.)