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

Author

M. F. Hasler, Jul 29 2015

Keywords

• nonn
• base
• hard
• more

Examples

			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.
		

Links

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

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.

Programs

PARI

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

Formula

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

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