A070821 - OEIS

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A070821

Integer part of n/(lpf(n)*gpf(n)), where lpf = A020639 is the least prime factor and gpf = A006530 the greatest prime factor.

1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 4, 0, 3, 0, 2, 1, 1, 0, 4, 1, 1, 3, 2, 0, 3, 0, 8, 1, 1, 1, 6, 0, 1, 1, 4, 0, 3, 0, 2, 3, 1, 0, 8, 1, 5, 1, 2, 0, 9, 1, 4, 1, 1, 0, 6, 0, 1, 3, 16, 1, 3, 0, 2, 1, 5, 0, 12, 0, 1, 5, 2, 1, 3, 0, 8, 9, 1, 0, 6, 1, 1, 1, 4, 0

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OFFSET

1,8

COMMENTS

m/(lpf(m)*gpf(m)) is an integer if and only if m is not prime;

a(m) = 0 iff m is prime (A000040);

for m > 1: a(m) = 1 iff m is semiprime (A001358).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = floor(A032742(n)/A006530(n)) = floor(A052126(n)/A020639(n)).

MATHEMATICA

a[n_] := With[{f = FactorInteger[n]},

Floor[n/(f[[1, 1]]*f[[-1, 1]])]];

Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 13 2023 *)

PROG

(Scheme) (define (A070821 n) (floor->exact (/ (A032742 n) (A006530 n)))) ;; See under A006530, A020639 and A032742 for further code. - Antti Karttunen, Aug 12 2017

CROSSREFS

Cf. A006530, A020639, A032742, A052126.

Sequence in context: A140748 A185305 A259875 * A165890 A051632 A278700

Adjacent sequences: A070818 A070819 A070820 * A070822 A070823 A070824

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 15 2002

STATUS

approved