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A065148
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Nonprimes m such that phi(m)*sigma(m) is divisible by m+1.
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1
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15, 20, 35, 95, 104, 143, 207, 255, 287, 319, 323, 464, 539, 650, 890, 899, 1023, 1034, 1199, 1295, 1349, 1407, 1519, 1763, 1952, 2015, 2204, 2834, 2975, 3599, 4031, 4454, 4607, 5183, 6479, 9215, 9503, 9799, 10403, 11339, 11663, 12095, 12824, 13055
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history;
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OFFSET
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1,1
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..500
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FORMULA
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A000010(m)*A000203(m) == 0 (mod m+1), m is composite.
(Every prime p satisfies A000010(p)*A000203(p) == 0 (mod p+1).)
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EXAMPLE
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m=95, phi(95)=72, sigma(95)=120, product=8640, product/(m+1)=90.
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MATHEMATICA
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Do[s=EulerPhi[n]*DivisorSigma[1, n]; If[IntegerQ[s/(n+1)]&&!PrimeQ[n], Print[n]], {n, 1, 100000}]
Select[Range[14000], !PrimeQ[#]&&Divisible[EulerPhi[#]DivisorSigma[1, #], #+1]&] (* Harvey P. Dale, Jul 08 2017 *)
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PROG
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(PARI) { n=0; for (m=1, 10^9, s=eulerphi(m)*sigma(m); if (s%(m+1) == 0 && !isprime(m), write("b065148.txt", n++, " ", m); if (n==500, return)) ) } \\ Harry J. Smith, Oct 12 2009
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CROSSREFS
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Cf. A000010, A000203, A062354, A011257.
Sequence in context: A088494 A109659 A294149 * A093028 A105506 A120625
Adjacent sequences: A065145 A065146 A065147 * A065149 A065150 A065151
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Oct 18 2001
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EXTENSIONS
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Offset changed from 0 to 1 by Harry J. Smith, Oct 12 2009
Definition clarified by Harvey P. Dale, Jul 08 2017
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STATUS
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approved
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