A100762 - OEIS

A100762

Let n = 2^e_2 * 3^e_3 * 5^e_5 * ... be the prime factorization of n and let P(n) = A100549(n); then a(n) = Product_{ q <= P(n) } q^e_q; a(1) = 1 by convention.

1, 2, 1, 4, 1, 2, 1, 8, 9, 2, 1, 12, 1, 2, 1, 16, 1, 18, 1, 4, 1, 2, 1, 24, 1, 2, 27, 4, 1, 2, 1, 32, 1, 2, 1, 36, 1, 2, 1, 8, 1, 2, 1, 4, 9, 2, 1, 48, 1, 2, 1, 4, 1, 54, 1, 8, 1, 2, 1, 12, 1, 2, 9, 64, 1, 2, 1, 4, 1, 2, 1, 72, 1, 2, 3, 4, 1, 2, 1, 80, 81, 2, 1, 12, 1, 2, 1, 8, 1, 18, 1, 4, 1, 2, 1, 96, 1

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

MAPLE

# First load the procedure pp from A100549

# B = prod_{p <= pp(n)} p^e_p

B := proc(n) local v, f, pv; global pp; option remember;

pv := pp(n);

v := 1:

for f in op(2..-1, ifactors(n)) while f[1] <= pv do

v := v * f[1]^f[2];

end do;

return v;

end proc;

MATHEMATICA

{1}~Join~Array[Function[{q, P}, Times @@ Power @@@ Select[q, First@# <= P &]] @@ {#, Prime@ PrimePi[1 + Max@ #[[All, -1]] ]} &@ FactorInteger[#] &, 96, 2] (* Michael De Vlieger, Nov 13 2018 *)

PROG

(PARI)

A100549(n) = if(1==n, 1, prime(primepi(1+vecmax(factor(n)[, 2]))));

A100762(n) = if(1==n, 1, my(u = A100549(n), f=factor(n)); prod(i=1, #f~, if(f[i, 1]<=u, f[i, 1]^f[i, 2], 1))); \\ Antti Karttunen, Nov 11 2018

CROSSREFS

Cf. A100549, A100417, A141586, A082725.

Sequence in context: A108738 A064405 A235872 * A059147 A091891 A258127

Adjacent sequences: A100759 A100760 A100761 * A100763 A100764 A100765

KEYWORD

nonn

AUTHOR

David Applegate and N. J. A. Sloane, Sep 15 2008

STATUS

approved