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A333352
a(n) is the product of indices of the smallest and greatest prime factors of n.
1
1, 1, 4, 1, 9, 2, 16, 1, 4, 3, 25, 2, 36, 4, 6, 1, 49, 2, 64, 3, 8, 5, 81, 2, 9, 6, 4, 4, 100, 3, 121, 1, 10, 7, 12, 2, 144, 8, 12, 3, 169, 4, 196, 5, 6, 9, 225, 2, 16, 3, 14, 6, 256, 2, 15, 4, 16, 10, 289, 3, 324, 11, 8, 1, 18, 5, 361, 7, 18, 4, 400, 2, 441, 12, 6, 8, 20, 6, 484, 3
OFFSET
1,3
FORMULA
If n = Product (p_j^k_j) then a(n) = min{pi(p_j)} * max{pi(p_j)}, where pi = A000720.
a(n) = A055396(n) * A061395(n) for n > 1.
a(2*n) = A061395(n) for n > 1.
a(n^k) = a(n) for k > 0
a(2*prime(n)^k) = n for k > 0.
a(prime(n)^k) = n^2 for k > 0.
a(n!) = pi(n) for n > 1.
a(A002110(n)) = n.
EXAMPLE
a(315) = a(3^2 * 5 * 7) = a(prime(2)^2 * prime(3) * prime(4)) = 2 * 4 = 8.
MATHEMATICA
a[1] = 1; a[n_] := PrimePi[FactorInteger[n] [[1, 1]]] PrimePi[ FactorInteger[ n] [[-1, 1]]]; Table[a[n], {n, 1, 80}]
PROG
(PARI) a(n) = if (n==1, 1, my(f=factor(n)[, 1]); primepi(vecmin(f))*primepi(vecmax(f))); \\ Michel Marcus, Mar 16 2020
CROSSREFS
Cf. A000079 (positions of 1's), A000720, A002110, A006530, A020639, A033845 (positions of 2's), A055396, A061395, A066048, A156061, A243055.
Sequence in context: A342446 A306744 A304526 * A260253 A376783 A261981
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 15 2020
STATUS
approved