A260588 Number of prime factors, counted with multiplicity, of A173426(n) = concatenation of (1, 2, ..., n, n-1, ..., 1).

0, 2, 4, 4, 4, 10, 4, 8, 8, 1, 2, 5, 3, 6, 7, 4, 5, 8, 6, 2, 6, 3, 4, 9, 2, 6, 11, 2, 4, 10, 4, 9, 8, 6, 6, 12, 3, 6, 8, 4, 6, 7, 3, 6

Offset

1,2

Links

Table of n, a(n) for n=1..44.

FactorDB, (121*10^(4*n-19) - 1002*10^(4*n-28) - 2*10^(2*n-9) + 879*10^10 + 121)/99^2.

Formula

a(n) = A001222(A173426(n)).

Example

a(2) = 2 since A173426(2) = 121 = 11*11 has twice the factor 11.
a(21) = 6 since A173426(21) = 3 * 3 * 7 * 828703 * 94364768151913037621 * 250591098443370396365457961250972909.

Prog

(PARI) a(n)=bigomega(A173426(n))

Crossrefs

See A260587 for the variant where only distinct prime factors are counted.

See also A075023 and A075024 for the smallest and largest prime factor of the terms.

Cf. A001222.

Sequence in context: A299768 A021413 A082855 * A107058 A332336 A101449

Adjacent sequences: A260585 A260586 A260587 * A260589 A260590 A260591

Keyword

nonn,base,hard,more

Author

M. F. Hasler, Jul 29 2015

Extensions

Terms beyond a(30) via factorization results by Serge Batalov, added by M. F. Hasler, Jul 30 2015

a(38)-a(44) added using factordb.com by Jinyuan Wang, Mar 05 2020

Status

approved