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A281707 Even integers k such that phi(sum of even divisors of k) = sum of odd divisors of k. 2
2, 6, 14, 42, 62, 186, 254, 434, 762, 1302, 1778, 5334, 7874, 16382, 23622, 49146, 55118, 114674, 165354, 262142, 344022, 507842, 786426, 1048574, 1523526, 1834994, 2080514, 3145722, 3554894, 5504982, 6241542, 7340018, 8126402, 10664682, 14563598, 22020054 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The number of divisors of a(n) is a power of 2, and sum of even divisors = 2^(m+1), sum of odd divisors = 2^m for some m.
a(n) == 2, 6 (mod 8) or a(n) == 2, 6 (mod 12).
a(n) is of the form 2*p1*p2*...pk where p1, p2, ..., pk are Mersenne primes = 3, 7, 31, 127, 8191, ... (see A000668).
LINKS
EXAMPLE
62 is a term because its divisors are 1, 2, 31 and 62, the sum of the even divisors of 62 = 62 + 2 = 2^6, the sum of odd divisors = 1 + 31 = 2^5, and phi(2^6) = 2^5.
MAPLE
with(numtheory):
for n from 2 by 2 to 10^6 do:
x:=divisors(n):n1:=nops(x):s0:=0:s1:=0:
for k from 1 to n1 do:
if irem(x[k], 2)=0
then
s0:=s0+ x[k]:
else
s1:=s1+ x[k]:
fi:
od:
if s1=phi(s0)
then
print(n):
else
fi:
od:
MATHEMATICA
Select[2 * Range[10^6], (sodd = (s = DivisorSigma[1, #])/(2^(IntegerExponent[#, 2]+1) - 1)) == EulerPhi[s - sodd] &] (* Amiram Eldar, Aug 12 2023 *)
PROG
(PARI) isok(n) = eulerphi(sumdiv(n, d, d*((d % 2)==0))) == sumdiv(n, d, d*(d%2)); \\ Michel Marcus, Jan 28 2017
CROSSREFS
Sequence in context: A008325 A004066 A123383 * A225172 A212197 A151414
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 28 2017
EXTENSIONS
a(1) inserted by Amiram Eldar, Aug 12 2023
STATUS
approved

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Last modified February 29 20:48 EST 2024. Contains 370428 sequences. (Running on oeis4.)