1,24

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).

M. F. Hasler, Table of n, a(n) for n = 1..10000

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

(PARI) A135767(n)=numdiv(n)-omega(n)-bigomega(n)

Cf. A102466, A102467 ; A001037, A107847.

Sequence in context: A116681 A131371 A003475 this_sequence A070203 A070201 A070138

Adjacent sequences: A135764 A135765 A135766 this_sequence A135768 A135769 A135770

easy,nonn

M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jan 14 2008