A358193 - OEIS

A358193

Denominator of the quotient of the prime indices of the n-th semiprime.

1, 2, 1, 3, 4, 3, 2, 5, 1, 6, 5, 7, 4, 8, 3, 9, 1, 7, 5, 4, 10, 11, 2, 9, 12, 5, 13, 7, 14, 5, 3, 11, 15, 8, 16, 6, 3, 17, 7, 1, 18, 13, 7, 2, 19, 15, 20, 6, 10, 21, 11, 22, 8, 9, 23, 1, 17, 24, 9, 4, 7, 25, 19, 26, 5, 13, 27, 8, 10, 28, 14, 11, 29, 21, 7, 30

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OFFSET

1,2

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..76.

EXAMPLE

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

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Denominator/@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 A358105, numerator A358104.

The numerator is A358192.

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, A032741, A128301, A215366, A289508, A289509, A296150, A300912, A318991, A358106.

Sequence in context: A301471 A237124 A233547 * A122530 A301453 A278340

Adjacent sequences: A358190 A358191 A358192 * A358194 A358195 A358196

KEYWORD

nonn,frac

AUTHOR

Gus Wiseman, Nov 03 2022

STATUS

approved