A333352 a(n) is the product of indices of the smallest and greatest prime factors of n.

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

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from indices in prime factorization

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 A261981 A153265

Adjacent sequences: A333349 A333350 A333351 * A333353 A333354 A333355

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 15 2020

Status

approved