A229027 Numbers n such that n/rad(n) equals the greatest prime dividing n.

4, 9, 18, 25, 49, 50, 75, 98, 121, 147, 150, 169, 242, 245, 289, 294, 338, 361, 363, 490, 507, 529, 578, 605, 722, 726, 735, 841, 845, 847, 867, 961, 1014, 1058, 1083, 1183, 1210, 1369, 1445, 1470, 1587, 1681, 1682, 1690, 1694, 1734, 1805, 1815, 1849, 1859

Offset

1,1

Comments

Numbers n such that n/A007947(n)= A006530(n) where A007947 is the product of the distinct prime factors of n and A006530 is the greatest prime dividing n.

The numbers of the form p^2 with p prime, or of the form p_1*p_2*...*p_k*p^2 with p_i primes < p prime are in the sequence.

All these numbers are round numbers (their greatest prime factor is <= their square root. - Emmanuel Vantieghem, Feb 22 2017

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Maple

with(numtheory) :for n from 2 to 2000 do:x:=factorset(n):n1:=nops(x): p:= product('x[i]', 'i'=1..n1):m:=n/p:if m=x[n1] then printf(`%d, `, n):else fi:od:

Mathematica

rad[n_]:=Times@@(First@#&/@FactorInteger@n); Select[Range[2, 2000], FactorInteger[#][[-1, 1]]==#/rad[#]&]
gpQ[n_]:=Module[{pf=Transpose[FactorInteger[n]][[1]]}, n/Times@@pf == Last[ pf]]; Select[Range[2, 2000], gpQ] (* Harvey P. Dale, Aug 16 2014 *)

Prog

(PARI) isok(n) = my(f = factor(n)); n/factorback(f[, 1]) == f[#f~, 1]; \\ Michel Marcus, Aug 16 2014

Crossrefs

Cf. A007947, A006530, A228957.

Sequence in context: A368780 A062952 A344405 * A100435 A160172 A256536

Adjacent sequences: A229024 A229025 A229026 * A229028 A229029 A229030

Keyword

nonn

Author

Michel Lagneau, Sep 11 2013

Status

approved