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
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
KEYWORD
easy,nonn
AUTHOR
M. F. Hasler, Jan 14 2008
STATUS
approved