A124877 -id:A124877 - cp's OEIS frontend

A124876 Number of prime factors (counted with multiplicity) in factorization of A007408(n).

0, 2, 1, 3, 2, 4, 3, 2, 3, 5, 3, 3, 3, 2, 1, 4, 2, 5, 1, 3, 2, 6, 2, 4, 2, 1, 3, 5, 3, 6, 1, 2, 3, 2, 3, 10, 4, 4, 5, 5, 8, 7, 7, 2, 4, 7, 3, 2, 4, 3, 2, 5, 3, 4, 2, 8, 3, 4, 4, 5, 3, 3, 7, 2, 5, 10, 4, 2, 6, 8, 3, 6, 6, 4, 3, 6, 4, 7, 4, 4, 3, 4, 8, 5, 7, 4

Offset: 1

M. F. Hasler, Nov 11 2006

nonn

			a(1) = 0 since A007408(1) = 1 contains no prime factor,
a(2) = 2 since A007408(2) = 9 = 3 * 3,
a(3) = 1 since A007408(3) = 251 is prime,
a(6) = 4 since A007408(6) = 7 * 7 * 11 * 53.

Amiram Eldar, Table of n, a(n) for n = 1..106

Cf. A001222, A007408, A124877, A124787.

seq( add(op(2,j),j=op(2,(ifactors@A007408)(n))), n=1..28 );
A001222 := proc(n) numtheory[bigomega](n) ; end: b := fscanf("b007408.txt","%d %d") : while b <> [] do printf("%d, ",A001222(op(2,b))) ; b := fscanf("b007408.txt","%d %d") : od : # R. J. Mathar, May 18 2007

Table[PrimeOmega[Numerator[Sum[1/k^3, {k, 1, n}]]], {n, 1, 50}] (* Amiram Eldar, Feb 09 2020 *)
PrimeOmega[Numerator[Accumulate[1/Range[50]^3]]] (* Harvey P. Dale, Aug 28 2023 *)

a(n) = A001222(A007408(n)). - R. J. Mathar, May 18 2007

More terms from R. J. Mathar, May 18 2007

More terms from Amiram Eldar, Feb 09 2020

A124874 Number of distinct primes dividing A007408(n).

Original entry on oeis.org

0, 1, 1, 3, 2, 3, 3, 2, 3, 4, 3, 2, 3, 2, 1, 3, 2, 4, 1, 3, 2, 5, 2, 4, 2, 1, 3, 4, 3, 5, 1, 2, 3, 2, 3, 8, 4, 4, 5, 4, 8, 6, 7, 2, 4, 6, 3, 2, 4, 3, 2, 4, 3, 4, 2, 8, 3, 3, 4, 4, 3, 3, 7, 2, 5, 9, 4, 2, 6, 7, 3, 5, 6, 4, 3, 6, 4, 6, 4, 4, 3, 3, 8, 5, 7, 4, 5

Offset: 1

M. F. Hasler, Nov 11 2006

nonn

			a(1) = 0 since no prime divides A007408(1) = 1,
a(2) = 1 since 3 is the only prime dividing A007408(2) = 9,
a(3) = 1 since A007408(3) = 251 is prime,
a(4) = 3 since A007408(4) = 5 * 11 * 37,
a(6) = 3 since 7, 11, 53 are the only primes dividing A007408(6) = 7^2 * 11 * 53.

Amiram Eldar, Table of n, a(n) for n = 1..106

Cf. A001221, A007408, A124876, A124877.

seq( (nops@op)(2,(ifactors@A007408)(n)),n=1..25);

Table[PrimeNu[Numerator[Sum[1/k^3, {k, 1, n}]]], {n, 1, 50}] (* Amiram Eldar, Feb 09 2020 *)

a(n) = A001221(A007408(n)).

More terms from Amiram Eldar, Feb 09 2020

A124875 Greatest prime dividing A007408(n).

Original entry on oeis.org

3, 251, 37, 5449, 53, 2591, 2538983, 462191, 4957, 5042929, 151099201553, 119465070161, 8868751511, 56154295334575853, 4480577578703, 1254664312327399, 34237559, 1683118856778495358491487, 294307265949353, 46956374669685791, 46572151, 110732345922475922393023393

Offset: 2

M. F. Hasler, Nov 11 2006

nonn

For all n>2, the exponent of a(n) in the factorization of A007408(n) appears to be 1.

			The offset is 2 since A007408(1) = 1 has no prime divisors at all.
a(2) = 3 is the largest prime dividing A007408(2) = 9,
a(3) = 251 is the largest prime dividing A007408(3) = 251,
a(4) = 37 since A007408(4) = 5 * 11 * 37.

Sean A. Irvine, Table of n, a(n) for n = 2..131 (a(50) corrected, Mar 14 2023, terms 2..106 from Amiram Eldar)

Cf. A007408, A124876, A124877.

seq(op([ -1,-2],op(-1,ifactors(A007408(n)))),n=2..25);

Table[FactorInteger[Numerator[Sum[1/k^3, {k, 1, n}]]][[-1, 1]], {n, 2, 20}] (* Amiram Eldar, Feb 09 2020 *)

a(n) = A006530(A007408(n)). - Amiram Eldar, Feb 09 2020

Data corrected and extended by Amiram Eldar, Feb 09 2020

cp's OEIS Frontend

A124876 Number of prime factors (counted with multiplicity) in factorization of A007408(n).

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A124874 Number of distinct primes dividing A007408(n).

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A124875 Greatest prime dividing A007408(n).

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