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A228301 Composite squarefree numbers n such that p-d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n. 5

%I

%S 6,10,14,15,35,70,154,190,322,385,442,595,682,2737,3619,14986,15314,

%T 19019,24817,26767,33626,78387,85034,130169,155363,166934,189727,

%U 214107,225029,238901,243217,285934,381547,395219,415679,417989,455609,466193,544918

%N Composite squarefree numbers n such that p-d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n.

%C Subsequence of A120944.

%H Donovan Johnson, <a href="/A228301/b228301.txt">Table of n, a(n) for n = 1..500</a>

%e Prime factors of 19019 are 7, 11, 13 and 19 while d(19019) = 16. We have that 19019 + 16 = 19035 and 19035 / (7 - 16) = -2115, 19035 / (11 - 16) = -3807, 19035 / (13 - 16) = -6345 and 19035 / (19 - 16) = 6345.

%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+tau(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(10^6);

%Y Cf. A000005, A228299, A228300, A228302.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Aug 20 2013

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

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Last modified August 5 22:03 EDT 2020. Contains 336214 sequences. (Running on oeis4.)