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A065656 Composite numbers k such that sigma(k)*phi(k) + 2*(k+1) is a square. 4
1169, 7777, 41111, 46097, 668167, 846817, 2107519, 3612769, 17424241, 30666527, 37526993, 56323393, 214746055, 383523857, 512376769, 1021934641, 1228492849, 1303949599, 4056001351, 7425397169, 17073544447, 17859428369, 18452226887, 46874737969, 51411954391 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) and square root of phi(a(n))*sigma(a(n)) + 2*a(n) + 2 are close to each other: e.g., a(7) = 2107519 and this square root is 2107458.

Since (p+1)*(p-1) + 2*(p+1) = p*p + 2*p + 1 = (p+1)^2 is a square, all primes are solutions.

73362272287 and 181264312447 are also terms. - Donovan Johnson, Jul 13 2012

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

k = 7777: sigma(7777) = 9792, phi(7777) = 6000 and 9792*6000 + 2*7778 = 587675556 = 7666^2.

PROG

(PARI) { n=0; for (m=1, 10^12, if (isprime(m), next); s=sigma(m)*eulerphi(m) + 2*(m + 1); if (issquare(s), write("b065656.txt", n++, " ", m); if (n==100, return)) ) } \\ Harry J. Smith, Oct 26 2009

CROSSREFS

Cf. A062354, A000203, A000010, A065655.

Sequence in context: A032744 A185477 A185469 * A185468 A209825 A264688

Adjacent sequences:  A065653 A065654 A065655 * A065657 A065658 A065659

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 12 2001

EXTENSIONS

a(9)-a(15) from Harry J. Smith, Oct 26 2009

a(16)-a(20) from Donovan Johnson, May 24 2011

a(21)-a(25) from Donovan Johnson, Jul 13 2012

STATUS

approved

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Last modified October 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)