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

Author

Gus Wiseman, Nov 20 2020

Keywords

• nonn

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.

Examples

			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, ...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

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.

Programs

Mathematica

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

Formula

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