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)[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
CROSSREFS
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