cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A242152 Numbers n such that the sum of their unitary prime divisors divides sigma(n).

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%I A242152 #19 Nov 26 2019 04:18:12
%S A242152 15,24,28,35,40,42,54,60,66,95,96,110,114,117,119,120,132,135,140,143,
%T A242152 147,168,195,198,209,224,240,250,252,258,280,287,290,315,319,322,323,
%U A242152 360,375,377,380,384,408,460,468,470,476,480,486,496,506,507,510,520
%N A242152 Numbers n such that the sum of their unitary prime divisors divides sigma(n).
%H A242152 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 A242152 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 A242152 with(numtheory): P:=proc(q) local a,b,k,n; for n from 1 to q do a:=divisors(n); b:=0;
%p A242152 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 A242152 if b>0 then if type(sigma(n)/b,integer) then print(n); fi; fi; od; end: P(10^10);
%t A242152 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 A242152 (PARI) isok(n) = (v = sumdiv(n, d, d*isprime(d)*(gcd(d, n/d)==1))) && ! (sigma(n) % v); \\ _Michel Marcus_, May 05 2014
%Y A242152 Cf. A000203, A063956.
%K A242152 nonn,easy
%O A242152 1,1
%A A242152 _Paolo P. Lava_, May 05 2014