A088613 Smallest nonsquarefree multiple of n.

4, 4, 9, 4, 20, 12, 28, 8, 9, 20, 44, 12, 52, 28, 45, 16, 68, 18, 76, 20, 63, 44, 92, 24, 25, 52, 27, 28, 116, 60, 124, 32, 99, 68, 140, 36, 148, 76, 117, 40, 164, 84, 172, 44, 45, 92, 188, 48, 49, 50, 153, 52, 212, 54, 220, 56, 171, 116, 236, 60, 244, 124, 63, 64, 260, 132

Offset

1,1

Links

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

Formula

If n is nonsquarefree, then a(n) = n. If n is an even squarefree integer, then a(n) = 2*n. If n is an odd squarefree multiple of 3, then a(n) = 3*n. If n is a squarefree integer not divisible by either 2 or 3, then a(n) = 4*n. a(p) = 4p if p is a prime >= 5. - Leroy Quet, May 14 2008

Sum_{k=1..n} a(k) ~ c * n^2, where c = 1/2 + 13/(2*Pi^2) = 1.158587... . - Amiram Eldar, Jul 02 2023

Mathematica

snmn[n_]:=Which[!SquareFreeQ[n], n, EvenQ[n], 2n, Mod[n, 3]==0, 3n, True, 4n]; Array[snmn, 70] (* Harvey P. Dale, Nov 11 2020 *)

Crossrefs

Cf. A013929.

Sequence in context: A023405 A160900 A035116 * A351582 A375544 A049723

Adjacent sequences: A088610 A088611 A088612 * A088614 A088615 A088616

Keyword

easy,nonn

Author

Amarnath Murthy, Oct 16 2003

Extensions

More terms from Ray Chandler, Oct 18 2003

Status

approved