

A285800


Numbers having more than one odd prime factor to an odd power in their prime factorization.


2



15, 21, 30, 33, 35, 39, 42, 51, 55, 57, 60, 65, 66, 69, 70, 77, 78, 84, 85, 87, 91, 93, 95, 102, 105, 110, 111, 114, 115, 119, 120, 123, 129, 130, 132, 133, 135, 138, 140, 141, 143, 145, 154, 155, 156, 159, 161, 165, 168, 170, 174, 177, 182, 183, 185, 186
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OFFSET

1,1


COMMENTS

The sequence is of asymptotic density one, a(n) ~ n.


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..19999


EXAMPLE

15 = 3*5, 21 = 3*7, 30 = 2*15, 33 = 3*11 are the smallest positive integers having at least two prime factors to an odd power in their factorization.
a(10) = 57, a(100) = 287, a(10^3) = 1950, a(10^4) = 15701, a(10^5) = 138540, a(10^6) = 1284998.


MAPLE

s800:=[]; s801:=[1];
for n from 2 to 1000 do
c:=0;
t2:=ifactors(n)[2];
for t3 in t2 do if t3[1]>2 and (t3[2] mod 2 = 1) then c:=c+1; fi; od:
if c <= 1 then s801:=[op(s801), n]; else s800:=[op(s800), n]; fi;
od:
s800; # A285800
s801; # A285801  N. J. A. Sloane, Sep 30 2017


PROG

(PARI) is(n)=1<#select(t>bittest(t, 0), factor(n>>valuation(n, 2))[, 2])


CROSSREFS

Subsequence of A248150.
Complement of A285801.
Sequence in context: A195527 A047200 A070537 * A184041 A070005 A275384
Adjacent sequences: A285797 A285798 A285799 * A285801 A285802 A285803


KEYWORD

nonn,easy


AUTHOR

M. F. Hasler, Apr 26 2017


STATUS

approved



