The number of 6-digit numbers of the form aba | vedclass

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(C) The $6$-digit number is of the form $ababab$.$ababab = 10^5 a + 10^4 b + 10^3 a + 10^2 b + 10a + b$$= (10^5 + 10^3 + 10)a + (10^4 + 10^2 + 1)b$$=

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$13$

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(C) The $6$-digit number is of the form $ababab$.$ababab = 10^5 a + 10^4 b + 10^3 a + 10^2 b + 10a + b$$= (10^5 + 10^3 + 10)a + (10^4 + 10^2 + 1)b$$= (101010)a + (10101)b = 10101(10a + b)$$= (3 	imes 7 	imes 13 	imes 37)(10a + b)$For the number to be a product of exactly $6$ distinct primes,$(10a + b)$ must be a product of $2$ distinct primes,and these primes must not be in the set $\{3, 7, 13, 37\}$.The possible values for $(10a + b)$ where $a \in \{1, 2, \dots, 9\}$ and $b \in \{0, 1, \dots, 9\}$ are numbers from $10$ to $99$.We check products of two distinct primes $p_1 	imes p_2$ such that $p_1, p_2 
otin \{3, 7, 13, 37\}$:$10 = 2 	imes 5$$14 = 2 	imes 7$ (contains $7$,invalid)$22 = 2 	imes 11$$26 = 2 	imes 13$ (contains $13$,invalid)$34 = 2 	imes 17$$38 = 2 	imes 19$$46 = 2 	imes 23$$55 = 5 	imes 11$$58 = 2 	imes 29$$62 = 2 	imes 31$$65 = 5 	imes 13$ (contains $13$,invalid)$74 = 2 	imes 37$ (contains $37$,invalid)$82 = 2 	imes 41$$85 = 5 	imes 17$$86 = 2 	imes 43$$91 = 7 	imes 13$ (contains $7, 13$,invalid)$94 = 2 	imes 47$$95 = 5 	imes 19$Counting the valid products: $10, 22, 34, 38, 46, 55, 58, 62, 82, 85, 86, 94, 95$. There are $13$ such numbers.

The number of $6$-digit numbers of the form $ababab$ (in base $10$) each of which is a product of exactly $6$ distinct primes is

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