select n, listagg(factor_exp, ' * ') within group (order by factor) factorization_of_n from
(select n, p factor, decode(max(m), 1, ''||p, p||'^'||max(m)) factor_exp from
(select level n from dual connect by level <= 100),
(select level m from dual connect by level < 7), -- 2^7 > 100
(select level + 1 p
from dual connect by level < 3
union all
select n from
(select 2 * level + 1 n from dual
connect by level <= 50) -- = 100/2
where
not exists
(select null from dual
where mod(n, 2*level + 1) = 0
connect by 2*level < sqrt(n)))
where n >= p
and mod(n, p) = 0
and mod(n, power(p,m)) = 0
group by n, p)
group by n
order by n;| N | FACTORIZATION_OF_N | 2 | 2 | 3 | 3 | 4 | 2^2 | 5 | 5 | 6 | 2 * 3 | 7 | 7 | 8 | 2^3 | 9 | 3^2 | 10 | 2 * 5 | 11 | 11 | 12 | 2^2 * 3 | 13 | 13 | 14 | 2 * 7 | 15 | 3 * 5 | 16 | 2^4 | 17 | 17 | 18 | 2 * 3^2 | 19 | 19 | 20 | 2^2 * 5 | 21 | 3 * 7 | 22 | 2 * 11 | 23 | 23 | 24 | 2^3 * 3 | 25 | 5^2 | 26 | 2 * 13 | 27 | 3^3 | 28 | 2^2 * 7 | 29 | 29 | 30 | 2 * 3 * 5 | 31 | 31 | 32 | 2^5 | 33 | 3 * 11 | 34 | 2 * 17 | 35 | 5 * 7 | 36 | 2^2 * 3^2 | 37 | 37 | 38 | 2 * 19 | 39 | 3 * 13 | 40 | 2^3 * 5 | 41 | 41 | 42 | 2 * 3 * 7 | 43 | 43 | 44 | 2^2 * 11 | 45 | 3^2 * 5 | 46 | 2 * 23 | 47 | 47 | 48 | 2^4 * 3 | 49 | 7^2 | 50 | 2 * 5^2 | 51 | 3 * 17 | 52 | 2^2 * 13 | 53 | 53 | 54 | 2 * 3^3 | 55 | 5 * 11 | 56 | 2^3 * 7 | 57 | 3 * 19 | 58 | 2 * 29 | 59 | 59 | 60 | 2^2 * 3 * 5 | 61 | 61 | 62 | 2 * 31 | 63 | 3^2 * 7 | 64 | 2^6 | 65 | 5 * 13 | 66 | 2 * 3 * 11 | 67 | 67 | 68 | 2^2 * 17 | 69 | 3 * 23 | 70 | 2 * 5 * 7 | 71 | 71 | 72 | 2^3 * 3^2 | 73 | 73 | 74 | 2 * 37 | 75 | 3 * 5^2 | 76 | 2^2 * 19 | 77 | 7 * 11 | 78 | 2 * 3 * 13 | 79 | 79 | 80 | 2^4 * 5 | 81 | 3^4 | 82 | 2 * 41 | 83 | 83 | 84 | 2^2 * 3 * 7 | 85 | 5 * 17 | 86 | 2 * 43 | 87 | 3 * 29 | 88 | 2^3 * 11 | 89 | 89 | 90 | 2 * 3^2 * 5 | 91 | 7 * 13 | 92 | 2^2 * 23 | 93 | 3 * 31 | 94 | 2 * 47 | 95 | 5 * 19 | 96 | 2^5 * 3 | 97 | 97 | 98 | 2 * 7^2 | 99 | 3^2 * 11 | 100 | 2^2 * 5^2 |
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