A285800 Numbers having more than one odd prime factor to an odd power in their prime factorization.

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

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: A047200 A070537 A324110 * A340380 A184041 A070005

Adjacent sequences: A285797 A285798 A285799 * A285801 A285802 A285803

Keyword

nonn,easy

Author

M. F. Hasler, Apr 26 2017

Status

approved