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

1,1

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A000010, A000203, A037074.

Sequence in context: A162280 A290781 A340449 * A212331 A067930 A257836

Adjacent sequences: A063529 A063530 A063531 * A063533 A063534 A063535

Keyword

nonn

Author

Labos Elemer, Aug 02 2001

Status

approved