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A303996 Numbers whose sum of divisors is the sixth power of one of their divisors. 6

%I #10 May 08 2018 02:43:56

%S 1,17490,19410,22578,2823492,162523452,165982908,216731788,221416468,

%T 221940628,226768440,230365560,232815480,234896520,238942920,

%U 240737160,241362120,242067720,242454120,242655720,258182910,264254670,268298190,272819070,277297710,286008510

%N Numbers whose sum of divisors is the sixth power of one of their divisors.

%C Subset of A019424.

%e Divisors of 17490 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 53, 55, 66, 106, 110, 159, 165, 265, 318, 330, 530, 583, 795, 1166, 1590, 1749, 2915, 3498, 5830, 8745, 17490 and their sum is 46656 = 6^6.

%p with(numtheory): P:=proc(q) local a,k,n;

%p for n from 1 to q do a:=sort([op(divisors(n))]);

%p for k from 1 to nops(a) do if sigma(n)=a[k]^6 then print(n); break; fi; od; od; end: P(10^9);

%o (PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 6) && !(n % sqrtnint(s, 6))); \\ _Michel Marcus_, May 05 2018

%Y Cf. A000203, A019424, A303123, A303993, A303994, A303995.

%K nonn,easy

%O 1,2

%A _Paolo P. Lava_, May 04 2018

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Last modified April 24 08:21 EDT 2024. Contains 371926 sequences. (Running on oeis4.)