A270539 - OEIS

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A270539

Primes p such that gcd(phi(p-1), sigma(p-1)) = 1 with phi = A000010, sigma = A000203.

2, 3, 5, 17, 37, 101, 257, 401, 577, 1297, 1601, 2917, 4357, 8101, 8837, 12101, 13457, 14401, 22501, 25601, 28901, 30977, 32401, 33857, 41617, 52901, 55697, 57601, 62501, 65537, 69697, 72901, 80657, 90001, 93637, 115601, 147457, 160001, 193601, 217157, 220901

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OFFSET

1,1

COMMENTS

Fermat primes (A019434) are terms.

LINKS

Jaroslav Krizek, Table of n, a(n) for n = 1..200

EXAMPLE

Prime 17 is a term because gcd(sigma(16), phi(16)) = gcd(31, 8) = 1.

PROG

(Magma) [n: n in [1..10^6] | IsPrime(n) and GCD(SumOfDivisors(n-1), EulerPhi(n-1)) eq 1]

(PARI) isok(p) = isprime(p) && (gcd(eulerphi(p-1), sigma(p-1)) == 1); \\ Michel Marcus, Oct 06 2021