A358192 Numerator of the quotient of the prime indices of the n-th semiprime.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 4, 1, 3, 1, 1, 2, 2, 1, 3, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 2, 1, 5, 3, 1, 3, 1, 1, 4, 1, 1, 2, 1, 1, 1, 5, 1, 2, 1, 2, 3, 1, 5, 1, 1, 3, 4, 1, 2, 6, 1, 1, 1, 3, 2, 5, 1, 1, 1, 3, 1, 1

Offset

1,6

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Table of n, a(n) for n=1..87.

Example

The 31st semiprime has prime indices (4,6), so the quotient is 4/6 = 2/3; hence a(31) = 2.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Numerator/@Divide@@@primeMS/@Select[Range[100], PrimeOmega[#]==2&]

Crossrefs

The divisible pairs are ranked by A318990, proper A339005.

The unreduced pair is (A338912, A338913).

The quotients of divisible pairs are A358103.

The restriction to divisible pairs is A358104, denominator A358105.

The denominator is A358193.

A000040 lists the primes.

A001222 counts prime indices, distinct A001221.

A001358 lists the semiprimes, squarefree A006881.

A003963 multiplies together prime indices.

A056239 adds up prime indices.

Cf. A000720, A027751, A128301, A215366, A289508, A289509, A296150, A300912, A318991, A358106.

Sequence in context: A287917 A325615 A029434 * A156281 A002217 A344173

Adjacent sequences: A358189 A358190 A358191 * A358193 A358194 A358195

Keyword

nonn,frac

Author

Gus Wiseman, Nov 03 2022

Status

approved