login
A349762
Numbers k such that phi(k) = A000010(k) is an abundant number (A005101) and d(k) = A000005(k) is a deficient number (A005100).
2
13, 19, 21, 25, 26, 27, 31, 33, 35, 36, 37, 38, 39, 41, 42, 43, 49, 54, 55, 56, 57, 61, 62, 65, 66, 67, 70, 71, 73, 74, 77, 78, 79, 81, 82, 86, 87, 88, 89, 91, 93, 95, 97, 100, 101, 103, 104, 105, 109, 110, 111, 112, 113, 114, 115, 119, 122, 123, 125, 127, 129
OFFSET
1,1
COMMENTS
Sándor (2005) proved that this sequence is infinite by showing that it includes all the numbers of the form 3^(p^2-1) where p is a prime.
LINKS
EXAMPLE
13 is a term since phi(13) = 12 is an abundant number, sigma(12) = 28 > 2*12 = 24, and d(13) = 2 is a deficient number, sigma(2) = 3 < 2*2 = 4.
MATHEMATICA
abQ[n_] := DivisorSigma[1, n] > 2*n; defQ[n_] := DivisorSigma[1, n] < 2*n; q[n_] := abQ[EulerPhi[n]] && defQ[DivisorSigma[0, n]]; Select[Range[150], q]
CROSSREFS
A164318 is a subsequence.
Sequence in context: A216639 A350301 A171098 * A118845 A050717 A335034
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 29 2021
STATUS
approved