A338913 Greater prime index of the n-th semiprime.

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

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.

After the first three terms, there appear to be no adjacent equal terms.

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 greater prime factors are:
  2, 3, 3, 5, 7, 5, 7, 11, 5, 13, ...
with indices:
  1, 2, 2, 3, 4, 3, 4, 5, 3, 6, ...
		

Links

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

Crossrefs

A115392 lists positions of first appearances of each positive integer.

A270652 is the squarefree case, with lesser part A270650.

A338898 has this as second column.

A338912 is the corresponding lesser prime index.

A001221 counts distinct prime indices.

A001222 counts prime indices.

A001358 lists semiprimes, with odd/even terms A046315/A100484.

A006881 lists squarefree semiprimes, with odd/even terms A046388/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, A084126, A084127, A112798, A128301, A289182, A320732, A320892, A338900, A338904, A338909.

Programs

Mathematica

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

Formula

a(n) = A000720(A084127(n)).