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 A228300 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 6,10,15,110,170,273,638,935,1394,2093,2438,2465,4823,5453,7973,11978,

%T 16354,17963,34918,43337,46943,62491,64583,68266,71603,72046,74347,

%U 75361,85877,134458,148291,155933,186235,188071,201994,209933,280891,307021,367081

%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="/A228300/b228300.txt">Table of n, a(n) for n = 1..500</a>

%e Prime factors of 17963 are 11, 23 and 71 while d(17963) = 8. We have that 17963 - 8 = 17955 and 17955 / (11 - 8) = 5985, 17955 / (23 - 8) = 1197 and 17955 / (71 - 8) = 285.

%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); ok:=1;

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

%p else if not type((n-tau(n))/(a[i]-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, A228301, 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 July 10 23:30 EDT 2020. Contains 335600 sequences. (Running on oeis4.)