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

1,1

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000203, A063956.

Sequence in context: A114558 A035408 A173035 * A269314 A269316 A081829

Adjacent sequences: A242149 A242150 A242151 * A242153 A242154 A242155

Keyword

nonn,easy

Author

Paolo P. Lava, May 05 2014

Status

approved