A253560 - OEIS

%I #21 Jun 27 2024 10:38:12

%S 1,4,9,8,25,18,49,16,27,50,121,36,169,98,75,32,289,54,361,100,147,242,

%T 529,72,125,338,81,196,841,150,961,64,363,578,245,108,1369,722,507,

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

%H Antti Karttunen, <a href="/A253560/b253560.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = 1; for n > 1, a(n) = A006530(n) * n = A000040(A061395(n)) * n.

%F Other identities:

%F a(n) >= A253550(n) for all n >= 1.

%F a(n) = A129598(n) for all n >= 2.

%F A052126(a(n)) = n. [A052126 works as an inverse function for this injection.]

%p A253560 := proc(n)

%p     n*A006530(n) # code re-use

%p end proc:

%p seq( A253560(n),n=1..80) ; # _R. J. Mathar_, Jun 27 2024

%t a[n_] := n FactorInteger[n][[-1, 1]];

%t Array[a, 100] (* _Jean-François Alcover_, Feb 15 2021 *)

%o (Scheme) (define (A253560 n) (* (A006530 n) n))

%o (PARI) a(n) = if (n==1, 1, n*vecmax(factor(n)[,1])); \\ _Michel Marcus_, Feb 15 2021

%Y Essentially the same as A129598, except that here we have a(1) = 1.

%Y Cf. A070003 (same sequence without 1, sorted into ascending order).

%Y Cf. A000040, A006530, A052126, A061395, A122111, A253550, A253561, A253563, A253565.

%Y Differs from A072995 for the first time at n=15, where a(15) = 75, while A072995(15) = 225.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 03 2015