A063532 Numbers k such that phi(k) + 1 = x^2 and sigma(k) + 1 = y^2 for some x and y.

15, 35, 56, 72, 78, 84, 123, 143, 165, 323, 543, 627, 678, 728, 814, 836, 899, 1350, 1484, 1535, 1683, 1763, 1846, 2296, 2967, 3288, 3444, 3599, 3784, 4103, 4620, 5084, 5183, 5964, 6580, 6693, 6820, 7150, 7626, 7806, 9096

Offset: 1

Author

Labos Elemer, Aug 02 2001

Keywords

• nonn

Examples

			If k = p(p+2) is a product of twin primes then phi(k) + 1 = p^2, sigma(k) + 1 = (p+2)^2, so k is in the sequence, A037074 a proper subset. There are many solutions not of this form, such as 72, 123, and 165.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000010, A000203, A037074.

Programs

PARI

{ n=0; for (a=1, 10^9, if (issquare(eulerphi(a) + 1) && issquare(sigma(a) + 1), write("b063532.txt", n++, " ", a); if (n==500, break)) ) } \\ Harry J. Smith, Aug 25 2009