A245303 Product of a prime and a power (exponent at least 2, base at least 1).

2, 3, 5, 7, 8, 11, 12, 13, 16, 17, 18, 19, 20, 23, 24, 27, 28, 29, 31, 32, 37, 40, 41, 43, 44, 45, 47, 48, 50, 52, 53, 54, 56, 59, 61, 63, 64, 67, 68, 71, 72, 73, 75, 76, 79, 80, 81, 83, 88, 89, 92, 96, 97, 98, 99, 101, 103, 104, 107, 108, 109, 112, 113, 116, 117, 124, 125, 127, 128, 131

Offset

1,1

Comments

Numbers of the form p*m^r where p prime, m > 0 and r > 1.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

72 is in this sequence because 72 = 2*36 = A000040(1)*A001597(9).
108 is in this sequence because 108 = 3*36 = A000040(2)*A001597(9).

Maple

filter:= proc(n) local E, ne, i, j;
  if isprime(n) then return true fi;
  E:= map(t->t[2], ifactors(n)[2]);
  ne:= nops(E);
  for j from 1 to ne do
     if igcd(seq(`if`(i=j, E[i]-1, E[i]), i=1..ne)) > 1 then return true fi;
  od;
  false
end proc:
filter(1):= false:
select(filter, [$1..1000]); # Robert Israel, Aug 11 2014

Prog

(PARI) ispp(n) = (n==1) || ispower(n);
isok(n) = {my(f = factor(n)); for (i=1, #f~, p = f[i, 1]; if (ispp(n/p), return(1)); ); return (0); } \\ Michel Marcus, Aug 08 2014

Crossrefs

Cf. A000040, A001597, A245661.

Sequence in context: A028743 A082634 A100959 * A359766 A166982 A026422

Adjacent sequences: A245300 A245301 A245302 * A245304 A245305 A245306

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 17 2014

Status

approved