A381959 Denominator of the sum of the reciprocals of the indices of distinct prime factors of n.

1, 1, 2, 1, 3, 2, 4, 1, 2, 3, 5, 2, 6, 4, 6, 1, 7, 2, 8, 3, 4, 5, 9, 2, 3, 6, 2, 4, 10, 6, 11, 1, 10, 7, 12, 2, 12, 8, 3, 3, 13, 4, 14, 5, 6, 9, 15, 2, 4, 3, 14, 6, 16, 2, 15, 4, 8, 10, 17, 6, 18, 11, 4, 1, 2, 10, 19, 7, 18, 12, 20, 2, 21, 12, 6, 8, 20, 3, 22, 3, 2, 13, 23, 4, 21, 14, 5, 5, 24, 6, 12, 9, 22, 15, 24

Offset

1,3

Links

Table of n, a(n) for n=1..95.

Index entries for sequences computed from indices in prime factorization

Formula

If n = Product (p_j^k_j) then a(n) = denominator of Sum (1/pi(p_j)).

G.f. for fractions: Sum_{k>=1} x^prime(k) / (k*(1 - x^prime(k))).

Example

0, 1, 1/2, 1, 1/3, 3/2, 1/4, 1, 1/2, 4/3, 1/5, 3/2, 1/6, 5/4, 5/6, 1, 1/7, 3/2, 1/8, 4/3, ...

Mathematica

Join[{1}, Table[Plus @@ (1/PrimePi[#[[1]]] & /@ FactorInteger[n]), {n, 2, 95}] // Denominator]
nmax = 95; CoefficientList[Series[Sum[x^Prime[k]/(k (1 - x^Prime[k])), {k, 1, nmax}], {x, 0, nmax}], x] // Denominator // Rest

Prog

(PARI) a(n) = my(f=factor(n)); denominator(sum(k=1, #f~, 1/primepi(f[k, 1]))); \\ Michel Marcus, Mar 11 2025

Crossrefs

Cf. A000720, A007947, A066328, A083346, A318574, A381958 (numerators).

Sequence in context: A364192 A253558 A061395 * A290103 A156061 A225395

Adjacent sequences: A381956 A381957 A381958 * A381960 A381961 A381962

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Mar 11 2025

Status

approved