A060700 "Anomalous" numbers k such that for even numbers 2k, gcd(2k, lcm(dd(2k)))=2k and not k, where dd(2k) is the first difference set of divisors of 2k.

15, 30, 35, 45, 63, 70, 75, 77, 91, 99, 105, 117, 126, 135, 140, 143, 150, 153, 154, 165, 175, 182, 187, 189, 195, 198, 209, 221, 225, 231, 234, 245, 247, 252, 255, 273, 280, 285, 286, 297, 299, 306, 308, 315, 323, 325, 330, 345, 350, 351, 357, 364, 374, 375

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

63 is here because for 126 = 2*63, lcm(dd(126)) = lcm(1, 1, 3, 1, 2, 5, 4, 3, 21, 21, 63) = 1260, so gcd(126, lcm(dd(126))) = gcd(126, 1260) = 126.

Prog

(PARI) f(n) = {my(d = divisors(n), dd = vector(#d-1, k, d[k+1] - d[k])); gcd(n, lcm(dd)); }
isok(n) = (f(2*n) == 2*n); \\ Michel Marcus, Mar 29 2018

Crossrefs

Cf. A060680, A060681, A060682, A060683, A060684, A060685, A060741, A060742, A060763, A060764, A060765, A060766, A000005.

Sequence in context: A291045 A079877 A215951 * A167210 A131933 A056917

Adjacent sequences: A060697 A060698 A060699 * A060701 A060702 A060703

Keyword

nonn

Author

Labos Elemer, Apr 25 2001

Status

approved