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

1,2

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A171561 A246551 A268391 * A186285 A190855 A190810

Adjacent sequences: A174892 A174893 A174894 * A174896 A174897 A174898

Keyword

nonn

Author

Jaroslav Krizek, Apr 01 2010

Extensions

Corrected by Jaroslav Krizek, Apr 02 2010

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

Status

approved