A338901 Position of the first appearance of prime(n) as a factor in the list of squarefree semiprimes.

1, 1, 2, 3, 6, 7, 9, 11, 13, 17, 18, 21, 23, 25, 29, 31, 34, 36, 40, 42, 45, 47, 50, 52, 56, 58, 61, 64, 67, 70, 76, 78, 81, 82, 86, 89, 93, 97, 100, 104, 106, 107, 112, 113, 116, 118, 125, 129, 133, 134, 135, 139, 141, 147, 150, 154, 159, 160, 165, 167, 169

Offset: 1

Author

Gus Wiseman, Nov 16 2020

Keywords

• nonn

Comments

The a(n)-th squarefree semiprime is the first divisible by prime(n).

After a(1) = 1, these are the positions of even terms in the list of all squarefree semiprimes A006881.

Links

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

Crossrefs

A001358 lists semiprimes, with odds A046315 and evens A100484.

A004526 counts 2-part partitions, with strict case A140106 (shifted left).

A005117 lists squarefree numbers.

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

A115392 is the not necessarily squarefree version.

A166237 gives the first differences of squarefree semiprimes.

A270650 and A270652 give the prime indices of squarefree semiprimes.

A320656 counts factorizations into squarefree semiprimes.

A338898 gives prime indices of semiprimes, with differences A176506.

A338899 gives prime indices of squarefree semiprimes, differences A338900.

A338912 and A338913 give the prime indices of semiprimes.

Cf. A001221, A001222, A002100, A056239, A065516, A112798, A167171, A320891, A320911, A338903, A338905.

Programs

Mathematica

rs=First/@FactorInteger[#]&/@Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&];
Table[Position[rs,i][[1,1]],{i,Union@@rs}]

Formula

A006881(a(n)) = A100484(n).