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A069249
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n^2-phi(n)*sigma(n).
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4
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0, 1, 1, 2, 1, 12, 1, 4, 3, 28, 1, 32, 1, 52, 33, 8, 1, 90, 1, 64, 57, 124, 1, 96, 5, 172, 9, 112, 1, 324, 1, 16, 129, 292, 73, 204, 1, 364, 177, 160, 1, 612, 1, 256, 153, 532, 1, 320, 7, 640, 297, 352, 1, 756, 145, 256, 369, 844, 1, 912, 1, 964, 225, 32, 193, 1476, 1, 592
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OFFSET
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1,4
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COMMENTS
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Always >0 for n>0. a(n)=1 if n is prime.
If p is a prime and k is a natural number then a(p^k)=p^(k-1) because a(p^k)=(p^k)^2-sigma(p^k)*phi(p^k) =p^(2k)-(p-1)*p^(k-1)*(p^(k+1)-1)/(p-1)=p^(k-1). If n is a composite number then a(n)>1 and a(1)=0, so n is prime iff a(n)=1. - Farideh Firoozbakht, Nov 15 2005
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = n^2-A062354(n). - R. J. Mathar, Oct 01 2011
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EXAMPLE
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sigma(10) = 18; phi(10) = 4; 10^2 - sigma(10)*phi(10) = 28. sigma(p) = p+1; phi(p) = p-1; p^2 - (p+1)(p-1) = 1. [From Walter Nissen, Aug 29 2009]
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MATHEMATICA
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Table[n^2-EulerPhi[n]DivisorSigma[1, n], {n, 70}] (* Harvey P. Dale, Oct 22 2016 *)
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PROG
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(PARI) a(n)=n^2-eulerphi(n)*sigma(n) \\ Charles R Greathouse IV, Nov 27 2013
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CROSSREFS
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Cf. A164875, A164876, A000203, A000010.
Sequence in context: A005730 A112284 A167401 * A128247 A161150 A163088
Adjacent sequences: A069246 A069247 A069248 * A069250 A069251 A069252
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre, Apr 13 2002
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STATUS
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approved
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