OFFSET
1,2
COMMENTS
First differs from A358817 at n = 165.
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 5, 38, 368, 3632, 36266, 362468, 3624664, 36246863, 362468411, 3624675258, ... . 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 0.36246... .
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter XIII, pp. 475-476.
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[300], FiniteAbelianGroupCount[#] == FiniteAbelianGroupCount[#+1] &]
PROG
(PARI) lista(kmax) = {my(c1 = 1, c2); for(k = 2, kmax, c2 = vecprod(apply(numbpart, factor(k)[, 2])); if(c1 == c2, print1(k-1, ", ")); c1 = c2); }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 15 2024
STATUS
approved