A360736 -id:A360736 - 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).

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, 4, 5, 8, 5, 6, 6, 3, 3, 7, 7, 7, 7, 10, 7, 6, 6, 7, 4, 5, 5, 7

Offset: 1

Bernard Schott, Mar 18 2023

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 * ...

			a(4) = 2 since 4321234 = 2 * 2160617;
a(6) = 3 since 65432123456 = 2^6 * 7 * 146053847.

M. Fleuren, Factoring of the Smarandache Mirror Sequence.
F. Smarandache, Only Problems, Not Solutions!, Mirror sequence, problem 19, page 20.

Cf. A001221, A007942, A110760, A360736.

from sympy import primefactors
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

a(n) = A001221(A007942(n)).

a(36)-a(54) from Amiram Eldar, Mar 19 2023
a(42) corrected by Sean A. Irvine, Sep 26 2023
a(55) from Sean A. Irvine, Oct 16 2023

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).

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