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A245303 Product of a prime and a power (exponent at least 2, base at least 1). 4
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 (list; graph; refs; listen; history; text; internal format)
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: A106735 A082634 A100959 * A166982 A026422 A026424

Adjacent sequences:  A245300 A245301 A245302 * A245304 A245305 A245306

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Jul 17 2014

STATUS

approved

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)