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

15, 24, 28, 35, 40, 42, 54, 60, 66, 95, 96, 110, 114, 117, 119, 120, 132, 135, 140, 143, 147, 168, 195, 198, 209, 224, 240, 250, 252, 258, 280, 287, 290, 315, 319, 322, 323, 360, 375, 377, 380, 384, 408, 460, 468, 470, 476, 480, 486, 496, 506, 507, 510, 520

Offset: 1

Author

Paolo P. Lava, May 05 2014

Keywords

• nonn
• easy

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paolo P. Lava)

Crossrefs

Cf. A000203, A063956.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,k,n; for n from 1 to q do a:=divisors(n); b:=0;
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;
if b>0 then if type(sigma(n)/b,integer) then print(n); fi; fi; od; end: P(10^10);

Mathematica

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 *)

PARI

isok(n) = (v = sumdiv(n, d, d*isprime(d)*(gcd(d, n/d)==1))) && ! (sigma(n) % v); \\ Michel Marcus, May 05 2014