A338912 Lesser prime index of the n-th semiprime.

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

Offset

1,3

Comments

A semiprime is a product of any two prime numbers. 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.

Formula

a(n) = A000720(A084126(n)).

Example

The semiprimes are:
  2*2, 2*3, 3*3, 2*5, 2*7, 3*5, 3*7, 2*11, 5*5, 2*13, ...
so the lesser prime factors are:
  2, 2, 3, 2, 2, 3, 3, 2, 5, 2, ...
with indices:
  1, 1, 2, 1, 1, 2, 2, 1, 3, 1, ...

Mathematica

Table[Min[PrimePi/@First/@FactorInteger[n]], {n, Select[Range[100], PrimeOmega[#]==2&]}]

Crossrefs

A084126 is the lesser prime factor (not index).

A084127 is the greater factor, with index A338913.

A115392 lists positions of ones.

A128301 lists positions of first appearances of each positive integer.

A270650 is the squarefree case, with greater part A270652.

A338898 has this as first column.

A001221 counts distinct prime indices.

A001222 counts prime indices.

A001358 lists semiprimes, with odds A046315 and evens A100484.

A006881 lists squarefree semiprimes, with odds A046388 and evens A100484.

A087794/A176504/A176506 are product/sum/difference of semiprime indices.

A338910/A338911 list products of pairs of odd/even-indexed primes.

Cf. A037143, A056239, A065516, A112798, A289182, A320732, A320892, A338900, A338904, A338909.

Sequence in context: A143323 A368542 A344234 * A086598 A211261 A344174

Adjacent sequences: A338909 A338910 A338911 * A338913 A338914 A338915

Keyword

nonn

Author

Gus Wiseman, Nov 20 2020

Status

approved