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
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, May 05 2014
STATUS
approved