A338913 - OEIS

%I #14 Sep 07 2024 08:54:23

%S 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,

%T 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,

%U 17,24,18,12,7,25,19,26,10,13,27,8,20,28,14,11,29,21

%N Greater prime index of the n-th semiprime.

%C 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.

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

%H Amiram Eldar, <a href="/A338913/b338913.txt">Table of n, a(n) for n = 1..10000</a>

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

%e The semiprimes are:

%e   2*2, 2*3, 3*3, 2*5, 2*7, 3*5, 3*7, 2*11, 5*5, 2*13, ...

%e so the greater prime factors are:

%e   2, 3, 3, 5, 7, 5, 7, 11, 5, 13, ...

%e with indices:

%e   1, 2, 2, 3, 4, 3, 4, 5, 3, 6, ...

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

%Y A115392 lists positions of first appearances of each positive integer.

%Y A270652 is the squarefree case, with lesser part A270650.

%Y A338898 has this as second column.

%Y A338912 is the corresponding lesser prime index.

%Y A001221 counts distinct prime indices.

%Y A001222 counts prime indices.

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

%Y A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.

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

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

%Y Cf. A037143, A056239, A065516, A084126, A084127, A112798, A128301, A289182, A320732, A320892, A338900, A338904, A338909.

%K nonn

%O 1,2

%A _Gus Wiseman_, Nov 20 2020