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Composite squarefree numbers n such that p-tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).
7

%I #21 Jan 16 2018 02:44:53

%S 6,10,15,22,78,138,273,483,3243,3913,104377,477337,1537627,1904487,

%T 2508961,3326829,3716167,5148949,6154017,6686113,11521842,14355679,

%U 16872583,25165777,28029883,31232337,32403342,50725419,57396469,68815381,86850249,98242959

%N Composite squarefree numbers n such that p-tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).

%C Subsequence of A120944.

%e Prime factors of 273 are 3, 7, 13 and sigma(273) = 448, tau(273) = 8.

%e 273 - 448 = -175 and (-175) / (3 - 8) = 35, (-175) / (7 - 8) = 175, (-175) / (13 - 8) = -35.

%p with (numtheory); P:=proc(q) local a, b, c, i, ok, p, n;

%p for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; ok:=1;

%p for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;

%p else if not type((n-sigma(n))/(a[i][1]-tau(n)), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(2*10^6);

%Y Cf. A000005, A000203.

%Y Cf. A228299, A228300, A228301, A228302, A229274, A229275, A229276.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Sep 19 2013

%E a(20)-a(33) from _Giovanni Resta_, Sep 20 2013

%E First term deleted by _Paolo P. Lava_, Sep 23 2013