A023897 -id:A023897 - cp's OEIS frontend

A147569 a(n) = sigma(A020492(n)).

1, 3, 4, 12, 28, 24, 24, 72, 48, 96, 120, 144, 168, 192, 336, 480, 360, 576, 480, 720, 720, 576, 720, 1344, 1440, 1440, 1440, 1872, 1728, 1920, 1680, 2880, 2016, 1440, 2880, 2880, 2880, 3600, 5760, 4320, 5040, 7200, 6720, 7392, 8064, 8640, 8640, 5760, 5616

Offset: 1

Enoch Haga, Nov 07 2008

			a(5) = sigma(A020492(5)) = sigma(12) = 28.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated from the b-file at A020492)

Cf. A020492, A023897, A147570.

[ SumOfDivisors(n): n in [1..3500] | SumOfDivisors(n) mod EulerPhi(n) eq 0 ]; // Klaus Brockhaus, Nov 09 2008

{for(n=1, 3500, a=sigma(n); if(a%eulerphi(n)==0, print1(a, ",")))} \\ Klaus Brockhaus, Nov 09 2008

Edited by Klaus Brockhaus, Nov 09 2008

A147570 a(n) = phi(A020492(n)).

Original entry on oeis.org

1, 1, 2, 2, 4, 6, 8, 8, 24, 12, 24, 24, 24, 48, 48, 48, 72, 48, 120, 80, 72, 192, 180, 96, 144, 180, 240, 144, 192, 240, 336, 192, 288, 720, 480, 360, 720, 720, 480, 720, 720, 720, 672, 672, 576, 720, 960, 1440, 1872, 1680, 960, 1120, 1848, 2016, 1440, 1728, 1440

Offset: 1

Enoch Haga, Nov 07 2008

			a(5) = phi(A020492(5)) = phi(12) = 4.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated from the b-file at A020492)

Cf. A000010 (Euler totient function phi(n)), A000203 (sigma(n), sum of divisors of n), A020492 (balanced numbers, numbers n such that phi(n) divides sigma(n)), A023897 (sigma(n) / phi(n) for balanced numbers), A147569.

[ a: n in [1..3500] | SumOfDivisors(n) mod a eq 0 where a is EulerPhi(n) ]; // Klaus Brockhaus, Nov 09 2008

{for(n=1, 5000, a=eulerphi(n); if(sigma(n)%a==0, print1(a, ",")))} \\ Klaus Brockhaus, Nov 09 2008

Edited by Klaus Brockhaus, Nov 09 2008

A063513 Least balanced numbers (A020492): m such that the quotient sigma(m)/phi(m) equals the n-th prime.

Original entry on oeis.org

3, 2, 56, 12, 2580, 630, 416640, 291060, 1719277560, 587133466920, 33044291280

Offset: 1

Labos Elemer, Jul 31 2001

			n=7: p(7) = 17. a(7) = 416640 = 2^7*3*5*7*31. sigma(416640) = 1566720 = 17*phi(a(7)). phi(416640) = 92160.

Cf. A055234 (smallest x such that sigma(x) = n*phi(x)), A000203, A000010, A020492, A023897.

a(n) = Min{x : A000203(x)/A000010(x) = p(n)} = Min{x : A023897(x) = p(n)}

More terms from Robert G. Wilson v, Aug 09 2001

a(10)-a(11) (from A055234) added by Donovan Johnson, Feb 03 2012

cp's OEIS Frontend

A147569 a(n) = sigma(A020492(n)).

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A147570 a(n) = phi(A020492(n)).

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Magma

PARI

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A063513 Least balanced numbers (A020492): m such that the quotient sigma(m)/phi(m) equals the n-th prime.

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Extensions