

A063532


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


3



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
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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: A187400 A162280 A290781 * A212331 A067930 A257836
Adjacent sequences: A063529 A063530 A063531 * A063533 A063534 A063535


KEYWORD

nonn


AUTHOR

Labos Elemer, Aug 02 2001


STATUS

approved



