A071312 - OEIS

A071312

Squarefree numbers k such that the largest prime factor of k is equal to the sum of the other prime factors of k.

30, 70, 286, 646, 1798, 3135, 3526, 3570, 6279, 7198, 8855, 8970, 10366, 10626, 10695, 11571, 16095, 16530, 17255, 17391, 20615, 20706, 20735, 20806, 23326, 24738, 24882, 26691, 28083, 31031, 36519, 36890, 38086, 38130, 41151, 41615

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OFFSET

1,1

COMMENTS

If k = p(1)*p(2)*...p(r) is in the sequence, where p(r) is the largest prime factor, then p(r) = p(1)+p(2)+...+p(r-1).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

20706 = 2*3*7*17*29 and 2+3+7+17 = 29 hence 20706 is in the sequence.

MATHEMATICA

Select[Range[40000], SquareFreeQ[#] && Plus @@ (f = FactorInteger[#][[;; , 1]]) == 2 * f[[-1]] &] (* Amiram Eldar, Apr 23 2022 *)

PROG

(PARI) for(n=2, 100000, if(issquarefree(n)*sum(i=1, omega(n)-1, component(component(factor(n), 1), i))==vecmax(factor(n, 1)), print1(n, ", ")))

CROSSREFS

Cf. A005117, A071141.

Sequence in context: A301900 A357854 A071141 * A071142 A218327 A259753

Adjacent sequences: A071309 A071310 A071311 * A071313 A071314 A071315

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Jun 11 2002

STATUS

approved