

A067350


Numbers n such that sigma(n)+phi(n) has exactly 4 divisors.


2



3, 5, 6, 7, 10, 11, 13, 16, 17, 19, 22, 23, 25, 27, 29, 31, 37, 40, 41, 43, 46, 47, 52, 53, 58, 59, 61, 64, 67, 68, 71, 72, 73, 79, 80, 82, 83, 89, 97, 98, 101, 103, 106, 107, 109, 113, 117, 127, 128, 131, 136, 137, 139, 144, 149, 151, 157, 162, 163, 166, 167, 169
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OFFSET

1,1


COMMENTS

For all terms up to 10^12, sigma(n)+phi(n) is a product of 2 distinct primes. The only other possibility is that sigma(n)+phi(n) is a cube of a prime, for some n which is either a square or twice a square; does this occur? If not, then this sequence is contained in A067351.


LINKS

Table of n, a(n) for n=1..62.


FORMULA

A000005(A000010(n)+A000203(n))=4=A067349(n)


EXAMPLE

Includes all odd primes and some composites; e.g. 22 and 25, since sigma(22)+phi(22)=36+10=46=2*23 and sigma(25)+phi(25)=31+20=51=3*17.


MATHEMATICA

Select[ Range[ 1, 200 ], DivisorSigma[ 0, DivisorSigma[ 1, # ]+EulerPhi[ # ] ]==4& ]


CROSSREFS

Cf. A000005, A000010, A000203, A067349, A067351.
Sequence in context: A176175 A157201 A067351 * A176651 A028727 A028762
Adjacent sequences: A067347 A067348 A067349 * A067351 A067352 A067353


KEYWORD

nonn


AUTHOR

Labos Elemer, Jan 17 2002


EXTENSIONS

Edited by Dean Hickerson, Jan 20 2002


STATUS

approved



