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A242152 Numbers n such that the sum of their unitary prime divisors divides sigma(n). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)