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

1, 4, 9, 8, 25, 18, 49, 16, 27, 50, 121, 36, 169, 98, 75, 32, 289, 54, 361, 100, 147, 242, 529, 72, 125, 338, 81, 196, 841, 150, 961, 64, 363, 578, 245, 108, 1369, 722, 507, 200, 1681, 294, 1849, 484, 225, 1058, 2209, 144, 343, 250, 867, 676, 2809, 162, 605, 392, 1083, 1682, 3481, 300, 3721, 1922, 441

Offset: 1

Author

Antti Karttunen, Jan 03 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

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

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

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

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

Programs

Maple

A253560 := proc(n)
    n*A006530(n) # code re-use
end proc:
seq( A253560(n),n=1..80) ; # R. J. Mathar, Jun 27 2024

Mathematica

a[n_] := n FactorInteger[n][[-1, 1]];
Array[a, 100] (* Jean-François Alcover, Feb 15 2021 *)

PARI

a(n) = if (n==1, 1, n*vecmax(factor(n)[,1])); \\ Michel Marcus, Feb 15 2021

Scheme

(define (A253560 n) (* (A006530 n) n))

Formula

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

Other identities:

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

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

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