cp's OEIS Frontend

A360736 Number of prime divisors of A007942(n) = decimal concatenation of sequence (n, n-1, ..., 2, 1, 2, ..., n-1, n) counted with multiplicity.

%I A360736 #26 Mar 23 2023 07:58:00
%S A360736 0,3,3,2,5,8,3,4,3,3,3,5,1,4,6,3,2,3,4,11,4,8,2,4,5,6,5,9,5,6,6,4,5,7,
%T A360736 4,8,8,5,7,7,3,3,7,9,7,7,10,8,6,7,7,10,5,5
%N A360736 Number of prime divisors of A007942(n) = decimal concatenation of sequence (n, n-1, ..., 2, 1, 2, ..., n-1, n) counted with multiplicity.
%C A360736 For n <= 1530, only a(13) = 1 (answer to Smaradanche problem 19).
%C A360736 First semiprimes appear in A007942 at indices 4, 17, 23 since a(4) = a(17) = a(23) = 2.
%H A360736 M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/SmMirror.txt">Factoring of the Smarandache Mirror Sequence</a>.
%H A360736 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>, Mirror sequence, problem 19, page 20.
%F A360736 a(n) = A001222(A007942(n)).
%e A360736 a(4) = 2 since 4321234 = 2 * 2160617;
%e A360736 a(6) = 8 since 65432123456 = 2^6 * 7 * 146053847;
%e A360736 a(12) = 5 since 12111098765432123456789101112 = 2^3*60800821*24899126702236725259;
%e A360736 a(13) = 1 since 131211109876543212345678910111213 is prime.
%o A360736 (Python)
%o A360736 from sympy import factorint
%o A360736 def A360736(n): return sum(factorint(int(''.join(map(str,range(n,1,-1)))+''.join(map(str,range(1,n+1))))).values()) # _Chai Wah Wu_, Mar 21 2023
%Y A360736 Cf. A001222, A007942, A110760, A361624.
%K A360736 nonn,base,more
%O A360736 1,2
%A A360736 _Bernard Schott_, Mar 18 2023
%E A360736 a(36)-a(54) from _Amiram Eldar_, Mar 19 2023