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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

%I

%S 4,9,4,25,55,49,9,25,49,121,253,49,529,129,121,125,515,133,961,121,25,

%T 529,1081,169,917,471,361,377,1711,121,2809,289,529,721,319,169,2831,

%U 1145,961,289,3403,497,49,529,361,1529,4811,289,841,781,1339,1369,5671,361

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

%C All terms are semiprimes or power of primes.

%H Paolo P. Lava, <a href="/A280441/b280441.txt">Table of n, a(n) for n = 0..165</a>

%e 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.

%p with(numtheory): P:=proc(q) local a,h,k,n; for n from 0 to q do for k from 1 to q do

%p if not isprime(k) then a:=sort([op(divisors(k))]);

%p 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)]});

%p if lcm(a)<k then print(k); break; fi; fi; od; od; end: P(10^6);

%Y Cf. A000961, A001358.

%K nonn

%O 0,1

%A _Paolo P. Lava_, Jan 03 2017

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Last modified January 17 14:57 EST 2020. Contains 330958 sequences. (Running on oeis4.)