A097215 Numbers m such that A076078(m) = m and bigomega(m) >= 2; or in other words, A097214, excluding powers of 2.
10, 44, 184, 752, 12224, 49024, 61064, 981520, 12580864, 206158168064, 16492668126208, 1080863908958322688, 18374686467592175488, 885443715520878608384, 4703919738602662723328, 226673591177468092350464, 232113757366000005450563584, 3894222643901120685369075227951104
Offset: 1
Keywords
Examples
For example, there are 184 sets of distinct positive integers with a least common multiple of 184.
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.
Crossrefs
Cf. A002235. - Farideh Firoozbakht, May 03 2009
Programs
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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 *) -
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; } 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
Extensions
More terms from Robert G. Wilson v, Aug 18 2004
More terms from Jinyuan Wang, Feb 11 2020
Comments