A174898 -id:A174898 - cp's OEIS frontend

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

Jaroslav Krizek, Apr 01 2010

nonn

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.

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

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

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

Corrected by Jaroslav Krizek, Apr 02 2010

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

A174897 a(n) = characteristic function of numbers k such that A007955(m) = k has solution for some m, where A007955(m) = product of divisors of m.

Original entry on oeis.org

1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0

Offset: 1

Jaroslav Krizek, Apr 01 2010

nonn

a(n) = characteristic function of numbers from A174895(n).

a(n) = 1 if A007955(m) = n for any m, else 0.

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for characteristic functions

Cf. A007955, A174895, A174898.

Block[{nn = 105, t}, t = ConstantArray[0, nn]; ReplacePart[t, Map[# -> 1 &, TakeWhile[Sort@ Array[Times @@ Divisors@ # &, nn], # <= 105 &]]]] (* Michael De Vlieger, Oct 20 2017 *)

up_to = 65537;
v174897 = vector(up_to);
A007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)); \\ This function from Charles R Greathouse IV, Feb 11 2011
for(k=1, up_to, t=A007955(k); if(t<=up_to, v174897[t] = 1));
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
write_to_bfile(1,v174897,"b174897_upto65537.txt");
\\ Antti Karttunen, Oct 20 2017

a(n) = 1 - A174898(n).

Name edited and more terms added by Antti Karttunen, Oct 20 2017

A174896 a(n) = numbers k in increasing order such that A007955(m) = k has no solution for any m, where A007955(m) = product of divisors of m.

Original entry on oeis.org

4, 6, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95

Offset: 1

Jaroslav Krizek, Apr 01 2010

nonn

Complement of A174895(n). A174897(a(n)) = 0, A174898(a(n)) = 1.

More terms from Michel Marcus, Sep 18 2013

cp's OEIS Frontend

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

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A174897 a(n) = characteristic function of numbers k such that A007955(m) = k has solution for some m, where A007955(m) = product of divisors of m.

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A174896 a(n) = numbers k in increasing order such that A007955(m) = k has no solution for any m, where A007955(m) = product of divisors of m.

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