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A253560 Multiply n by its largest prime factor: a(n) = A006530(n) * n.

%I A253560 #21 Jun 27 2024 10:38:12
%S A253560 1,4,9,8,25,18,49,16,27,50,121,36,169,98,75,32,289,54,361,100,147,242,
%T A253560 529,72,125,338,81,196,841,150,961,64,363,578,245,108,1369,722,507,
%U A253560 200,1681,294,1849,484,225,1058,2209,144,343,250,867,676,2809,162,605,392,1083,1682,3481,300,3721,1922,441
%N A253560 Multiply n by its largest prime factor: a(n) = A006530(n) * n.
%H A253560 Antti Karttunen, <a href="/A253560/b253560.txt">Table of n, a(n) for n = 1..10000</a>
%F A253560 a(1) = 1; for n > 1, a(n) = A006530(n) * n = A000040(A061395(n)) * n.
%F A253560 Other identities:
%F A253560 a(n) >= A253550(n) for all n >= 1.
%F A253560 a(n) = A129598(n) for all n >= 2.
%F A253560 A052126(a(n)) = n. [A052126 works as an inverse function for this injection.]
%p A253560 A253560 := proc(n)
%p A253560     n*A006530(n) # code re-use
%p A253560 end proc:
%p A253560 seq( A253560(n),n=1..80) ; # _R. J. Mathar_, Jun 27 2024
%t A253560 a[n_] := n FactorInteger[n][[-1, 1]];
%t A253560 Array[a, 100] (* _Jean-François Alcover_, Feb 15 2021 *)
%o A253560 (Scheme) (define (A253560 n) (* (A006530 n) n))
%o A253560 (PARI) a(n) = if (n==1, 1, n*vecmax(factor(n)[,1])); \\ _Michel Marcus_, Feb 15 2021
%Y A253560 Essentially the same as A129598, except that here we have a(1) = 1.
%Y A253560 Cf. A070003 (same sequence without 1, sorted into ascending order).
%Y A253560 Cf. A000040, A006530, A052126, A061395, A122111, A253550, A253561, A253563, A253565.
%Y A253560 Differs from A072995 for the first time at n=15, where a(15) = 75, while A072995(15) = 225.
%K A253560 nonn
%O A253560 1,2
%A A253560 _Antti Karttunen_, Jan 03 2015