A242152 - OEIS

%I #19 Nov 26 2019 04:18:12

%S 15,24,28,35,40,42,54,60,66,95,96,110,114,117,119,120,132,135,140,143,

%T 147,168,195,198,209,224,240,250,252,258,280,287,290,315,319,322,323,

%U 360,375,377,380,384,408,460,468,470,476,480,486,496,506,507,510,520

%N Numbers n such that the sum of their unitary prime divisors divides sigma(n).

%H Amiram Eldar, <a href="/A242152/b242152.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Paolo P. Lava)

%e Divisors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Its unitary prime divisors are 5 and 7. Finally, sigma(315) = 624 and 624 / (5 + 7) = 52.

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

%p for k from 1 to nops(a) do if isprime(a[k]) then if gcd(a[k],n/a[k])=1 then b:=b+a[k]; fi; fi; od;

%p if b>0 then if type(sigma(n)/b,integer) then print(n); fi; fi; od; end: P(10^10);

%t unitaryPrimeSum[1]=0; unitaryPrimeSum[n_] := Total[(f = FactorInteger[n])[[;;,1]] * (Boole[# == 1]& /@ f[[;;,2]])]; Select[Range[500], (ups = unitaryPrimeSum[#]) > 0 && Divisible[DivisorSigma[1, #], ups] &] (* _Amiram Eldar_, Nov 26 2019 *)

%o (PARI) isok(n) = (v = sumdiv(n, d, d*isprime(d)*(gcd(d, n/d)==1))) && ! (sigma(n) % v); \\ _Michel Marcus_, May 05 2014

%Y Cf. A000203, A063956.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, May 05 2014