OFFSET
1,1
COMMENTS
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 1, 15, 150, 1548, 15499, 154916, 1549105, 15489932, 154901767, 1549014294, ... . From these values the asymptotic density of this sequence, whose existence was proven by Erdős and Ivić (1987) (the constant c in the Formula section), can be empirically evaluated by 0.15490... .
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter XIII, p. 476.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős and Aleksandar Ivić, The distribution of values of a certain class of arithmetic functions at consecutive integers, Colloq. Math. Soc. János Bolyai, 51, Number Theory, Budapest, 1987, pp. 45-91. See p. 60.
FORMULA
The number of terms not exceeding x, N(x) = c * x + O(x^(3/4) * log(x)^4), where c > 0 is a constant (Erdős and Ivić, 1987).
MATHEMATICA
Select[Range[350], FiniteAbelianGroupCount[#] == PrimeOmega[#+1] - PrimeNu[#+1] &]
PROG
(PARI) is(n) = vecprod(apply(numbpart, factor(n)[, 2])) == bigomega(n+1) - omega(n+1);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 15 2024
STATUS
approved