

A280441


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


1



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
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OFFSET

0,1


COMMENTS

All terms are semiprimes or power of primes.


LINKS

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


EXAMPLE

a(36) = 2831 because 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



