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 A135767 sigma_0(n)-omega(n)-Omega(n) (sigma_0 = A000005 = # divisors, omega = A001221 = # prime factors, Omega = A001222 = # prime factors with multiplicity). 3
 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 2, 0, 1, 1, 0, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 5, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 0, 5, 0, 0, 1, 1, 0, 2, 0, 3, 0, 0, 0, 5, 0, 0, 0, 2, 0, 5, 0, 1, 0, 0, 0, 4, 0, 1, 1, 3, 0, 2, 0, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,24 COMMENTS A102467 = { n | a(n)>0 } ; A102466 = { n | a(n)=0 } = { n | omega(n)=1 or Omega(n)=2 }: these are exactly the prime powers (>1) and semiprimes. For all other numbers a(n) > 0 since for each of the Omega(n) prime power divisors, other divisors are obtained by multiplying it with another prime factor, which gives more than omega(n) different additional divisors. a(n)>0 is also equivalent to A001037(n) > A107847(n), i.e. there are strictly fewer nonzero sums of non-periodic subsets of U_n (n-th roots of unity) than there are non-periodic binary words of length n. Otherwise stated, a(n)>0 if there is a non-periodic subset of U_n with zero sum. Non-periodic means having no rotational symmetry (except for identity). LINKS M. F. Hasler, Table of n, a(n) for n = 1..10000 FORMULA a(n)=0 <=> omega(n)=1 or Omega(n)=2 <=> n is semiprime or a prime power (>1) <=> A001037(n) = A107847(n) <=> all non-periodic subsets of U_n have nonzero sum MATHEMATICA a[n_] := DivisorSigma[0, n] - PrimeOmega[n] - PrimeNu[n]; Array[a, 105] (* Jean-François Alcover, Jun 21 2018 *) PROG (PARI) A135767(n)=numdiv(n)-omega(n)-bigomega(n) CROSSREFS Cf. A102466, A102467 ; A001037, A107847. Sequence in context: A248639 A293959 A333146 * A208575 A070203 A070201 Adjacent sequences:  A135764 A135765 A135766 * A135768 A135769 A135770 KEYWORD easy,nonn AUTHOR M. F. Hasler, Jan 14 2008 STATUS approved

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Last modified April 6 02:43 EDT 2020. Contains 333267 sequences. (Running on oeis4.)