A100493 a(n) = n + n-th semiprime.

5, 8, 12, 14, 19, 21, 28, 30, 34, 36, 44, 46, 48, 52, 54, 62, 66, 69, 74, 77, 79, 84, 88, 93, 99, 103, 109, 113, 115, 117, 122, 125, 127, 129, 141, 147, 152, 156, 158, 161, 163, 165, 172, 177, 179, 187, 189, 191, 194, 196, 206, 210, 212, 215, 221, 225, 234, 236

Offset

1,1

Comments

This is the semiprime analog of A014688.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein, World of Mathematics, Semiprime.

Formula

a(n) = n + A001358(n).

a(n) ~ n log n / log log n. [Charles R Greathouse IV, Dec 28 2011]

Example

a(7) = 7 + semiprime(7) = 7 + 21 = 28.

Maple

N:= 1000: # to use semiprimes <= N
Primes:= select(isprime, [2, seq(i, i=3..N, 2)]):
Semiprimes:= sort(convert(select(`<=`, {seq(seq(Primes[i]*Primes[j], i=1..j), j=1..nops(Primes))}, N), list)):
seq(i+Semiprimes[i], i=1..nops(Semiprimes)); # Robert Israel, Dec 20 2015

Mathematica

m=300;
A001358:= A001358= Select[Range[5*m], PrimeOmega[#]==2 &];
A100493[n_]:= n + A001358[[n]];
Table[A100493[n], {n, m}] (* G. C. Greubel, Apr 04 2023 *)

Prog

(Magma)
m:=300;
A001222:=[n eq 1 select 0 else (&+[p[2]: p in Factorization(n)]): n in [1..4*m]];
A001358:=[n: n in [1..4*m] | A001222[n] eq 2];
A100493:= func< n | n + A001358[n] >;
[A100493(n): n in [1..m]]; // G. C. Greubel, Apr 04 2023
(SageMath)
from sympy import primeomega
b=[n for n in (1..1000) if primeomega(n)==2]
[n+b[n-1] for n in range(1, 301)] # G. C. Greubel, Apr 04 2023

Crossrefs

Cf. A001358, A014688, A100466, A100467, A100915, A100916.

Sequence in context: A066299 A278040 A161394 * A005661 A190773 A212452

Adjacent sequences: A100490 A100491 A100492 * A100494 A100495 A100496

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 20 2004

Extensions

Edited, corrected and extended by Ray Chandler, Nov 26 2004

Status

approved