cp's OEIS Frontend

A338912 Lesser prime index of the n-th semiprime.

%I A338912 #11 Sep 07 2024 08:54:19
%S A338912 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,
%T A338912 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,
%U A338912 2,1,3,4,1,2,6,1,3,2,6,2,5,1,4,1,3,2,1
%N A338912 Lesser prime index of the n-th semiprime.
%C A338912 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.
%H A338912 Amiram Eldar, <a href="/A338912/b338912.txt">Table of n, a(n) for n = 1..10000</a>
%F A338912 a(n) = A000720(A084126(n)).
%e A338912 The semiprimes are:
%e A338912   2*2, 2*3, 3*3, 2*5, 2*7, 3*5, 3*7, 2*11, 5*5, 2*13, ...
%e A338912 so the lesser prime factors are:
%e A338912   2, 2, 3, 2, 2, 3, 3, 2, 5, 2, ...
%e A338912 with indices:
%e A338912   1, 1, 2, 1, 1, 2, 2, 1, 3, 1, ...
%t A338912 Table[Min[PrimePi/@First/@FactorInteger[n]],{n,Select[Range[100],PrimeOmega[#]==2&]}]
%Y A338912 A084126 is the lesser prime factor (not index).
%Y A338912 A084127 is the greater factor, with index A338913.
%Y A338912 A115392 lists positions of ones.
%Y A338912 A128301 lists positions of first appearances of each positive integer.
%Y A338912 A270650 is the squarefree case, with greater part A270652.
%Y A338912 A338898 has this as first column.
%Y A338912 A001221 counts distinct prime indices.
%Y A338912 A001222 counts prime indices.
%Y A338912 A001358 lists semiprimes, with odds A046315 and evens A100484.
%Y A338912 A006881 lists squarefree semiprimes, with odds A046388 and evens A100484.
%Y A338912 A087794/A176504/A176506 are product/sum/difference of semiprime indices.
%Y A338912 A338910/A338911 list products of pairs of odd/even-indexed primes.
%Y A338912 Cf. A037143, A056239, A065516, A112798, A289182, A320732, A320892, A338900, A338904, A338909.
%K A338912 nonn
%O A338912 1,3
%A A338912 _Gus Wiseman_, Nov 20 2020