cp's OEIS Frontend

A361624 Number of distinct prime factors in decimal concatenation of integer (n, n-1, ..., 2, 1, 2, ..., n-1, n) = A007942(n).

%I A361624 #30 Oct 16 2023 22:28:30
%S A361624 0,2,3,2,5,3,3,4,3,3,3,3,1,4,6,2,2,3,4,7,4,8,2,3,4,6,5,7,5,6,6,3,5,7,
%T A361624 4,5,8,5,6,6,3,3,7,7,7,7,10,7,6,6,7,4,5,5,7
%N A361624 Number of distinct prime factors in decimal concatenation of integer (n, n-1, ..., 2, 1, 2, ..., n-1, n) = A007942(n).
%C A361624 a(n) < A360736(n) when n > 10 is a multiple of 4 or of 25, since, for these indices, A007942(n) is divisible by 2^2 or 5^2; but this inequality holds also, for other indices: for n = 6 (see example) and n = 39 where A007942(39) = 29 * 617^2 * 10185403128074353 * ...
%H A361624 M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/SmMirror.txt">Factoring of the Smarandache Mirror Sequence</a>.
%H A361624 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>, Mirror sequence, problem 19, page 20.
%F A361624 a(n) = A001221(A007942(n)).
%e A361624 a(4) = 2 since 4321234 = 2 * 2160617;
%e A361624 a(6) = 3 since 65432123456 = 2^6 * 7 * 146053847.
%o A361624 (Python)
%o A361624 from sympy import primefactors
%o A361624 def A361624(n): return len(primefactors(int(''.join(map(str,range(n,1,-1)))+''.join(map(str,range(1,n+1)))))) # _Chai Wah Wu_, Mar 21 2023
%Y A361624 Cf. A001221, A007942, A110760, A360736.
%K A361624 nonn,base,more
%O A361624 1,2
%A A361624 _Bernard Schott_, Mar 18 2023
%E A361624 a(36)-a(54) from _Amiram Eldar_, Mar 19 2023
%E A361624 a(42) corrected by _Sean A. Irvine_, Sep 26 2023
%E A361624 a(55) from _Sean A. Irvine_, Oct 16 2023