A280441 Least composite numbers k such that the least common multiples of their aliquot parts, each one increased by n, is less than k.

4, 9, 4, 25, 55, 49, 9, 25, 49, 121, 253, 49, 529, 129, 121, 125, 515, 133, 961, 121, 25, 529, 1081, 169, 917, 471, 361, 377, 1711, 121, 2809, 289, 529, 721, 319, 169, 2831, 1145, 961, 289, 3403, 497, 49, 529, 361, 1529, 4811, 289, 841, 781, 1339, 1369, 5671, 361

Offset

0,1

Comments

All terms are semiprimes or powers of primes.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..165

Example

a(36) = 2831 because the aliquot parts of 2831 are 1, 19, 149 and lcm(1 + 36, 19 + 36, 149 + 36) = lcm(37, 55, 185) = 2035 and 2831 is the least composite number to have this property.

Maple

with(numtheory): P:=proc(q) local a, h, k, n; for n from 0 to q do for k from 1 to q do
if not isprime(k) then a:=sort([op(divisors(k))]);
for h from 1 to nops(a)-1 do a[h]:=a[h]+n; od; a:={op(a)}; a:=op(a minus {a[nops(a)]});
if lcm(a)<k then print(k); break; fi; fi; od; od; end: P(10^6);

Crossrefs

Cf. A000961, A001358.

Sequence in context: A087321 A053143 A068238 * A255290 A087369 A200629

Adjacent sequences: A280438 A280439 A280440 * A280442 A280443 A280444

Keyword

nonn

Author

Paolo P. Lava, Jan 03 2017

Status

approved