OFFSET
1,5
FORMULA
a(n) = Sum_{k=1..n} [Omega(k*(2*n-k)) = 2] * [floor(log_10(k)) = floor(log_10(2*n-k))], where [ ] is the Iverson bracket and Omega is the number of prime factors of n with multiplicity (A001222).
EXAMPLE
a(18) = 0; 18 has 9 partitions into two positive integer parts, (17,1), (16,2), (15,3), (14,4), (13,5), (12,6), (11,7), (10,8), (9,9). There are no partitions whose parts have the same number of decimal digits and whose product is semiprime.
MATHEMATICA
Table[Sum[KroneckerDelta[PrimeOmega[i (2 n - i)], 2] KroneckerDelta[ Floor[Log10[i]], Floor[Log10[2 n - i]]], {i, n}], {n, 100}]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Wesley Ivan Hurt, Dec 21 2020
STATUS
approved