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A349760
Numbers k such that d(k) = A000005(k), sigma(k) = A000203(k) and phi(k) = A000010(k) are all abundant numbers (A005101).
2
84, 90, 108, 126, 132, 140, 150, 156, 180, 198, 220, 224, 228, 234, 252, 260, 276, 294, 300, 306, 308, 315, 336, 342, 348, 350, 352, 360, 364, 372, 380, 396, 414, 416, 420, 432, 444, 460, 476, 486, 490, 492, 495, 500, 504, 516, 522, 525, 528, 532, 540, 550, 558
OFFSET
1,1
COMMENTS
Sándor (2005) proved that this sequence is infinite by showing that it includes all the numbers of the form 11 * p^11 * k where p != 11 is a prime and k is any number coprime to 11*p.
LINKS
EXAMPLE
84 is a term since d(84) = 12, sigma(84) = 224 and phi(84) = 24 are all abundant numbers: sigma(12) = 28 > 2*12 = 24, sigma(224) = 504 > 2*224 = 448 and sigma(24) = 60 > 2*24 = 48.
MATHEMATICA
abQ[n_] := DivisorSigma[1, n] > 2*n; q[n_] := And @@ abQ /@ Join[DivisorSigma[{0, 1}, n], {EulerPhi[n]}]; Select[Range[500], q]
PROG
(PARI) isab(k) = sigma(k) > 2*k; \\ A005101
isok(k) = my(f=factor(k)); isab(numdiv(f)) && isab(sigma(f)) && isab(eulerphi(f)); \\ Michel Marcus, Dec 03 2021
CROSSREFS
Subsequence of A349758.
Sequence in context: A128873 A095607 A068405 * A045569 A219183 A289218
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 29 2021
STATUS
approved