A174895 a(n) = possible values of A007955(m) in increasing order, where A007955(m) = product of divisors of m.

1, 2, 3, 5, 7, 8, 11, 13, 17, 19, 23, 27, 29, 31, 36, 37, 41, 43, 47, 53, 59, 61, 64, 67, 71, 73, 79, 83, 89, 97, 100, 101, 103, 107, 109, 113, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 196, 197, 199, 211, 223, 225, 227, 229, 233, 239

Offset: 1

Author

Jaroslav Krizek, Apr 01 2010

Keywords

• nonn

Comments

a(n) = all values of A007955(m) in increasing order; all terms of sequence A007955 occur only once. Complement of A174896(n). A174897(a(n)) = 1, A174898(a(n)) = 0.

For every prime p, p and p^3 occur, as does the square of every semiprime pq with p and q distinct. - T. D. Noe, Oct 22 2010

For every prime p, every power p^t occurs, where t is a triangular number.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Programs

Mathematica

nn=1000; Reap[Do[prod=Times@@Divisors[n]; If[prod<=nn, Sow[prod]], {n,nn}]][[2,1]] (* T. D. Noe, Oct 22 2010 *)

PARI

list(lim)=my(v=List(primes([2,lim]))); for(k=1,sqrtint(lim\=1), listput(v,factorback(divisors(k)))); forprime(p=2,sqrtnint(lim,3), listput(v, p^3)); select(k->k<=lim, Set(v)) \\ Charles R Greathouse IV, Sep 22 2015

Extensions

Corrected by Jaroslav Krizek, Apr 02 2010

Corrected and extended by T. D. Noe, Oct 22 2010