A063836 Numbers k such that usigma(sigma(k)) is prime.

3, 217, 57337

Offset: 1

Author

Robert G. Wilson v, Aug 21 2001

Keywords

• nonn
• hard
• bref

Comments

Also, numbers k such that sigma(k) + 1 is a Fermat prime (A019434). Equivalently, numbers k that are a product of distinct Mersenne primes (A000668), k = (2^p_1 - 1) * (2^p_2 - 1) * ... * (2^p_m - 1), p_i are in A000043 and m >= 1, such that p_1 + p_2 + ... + p_m = 2^s and 2^(2^s) + 1 is prime. - Amiram Eldar, Jan 25 2025

Crossrefs

Cf. A000043, A000203, A000668, A019434, A034448, A061765, A063103.

Subsequence of A046528.

Programs

Mathematica

us[n_Integer] := (d = Divisors[n]; l = Length[d]; k = 1; s = n; While[k < l, If[ GCD[ d[[k]], n/d[[k]] ] == 1, s = s + d[[k]]]; k++ ]; s); Do[m = n; If[ PrimeQ[ us[ DivisorSigma[1, n]]], Print[n]], {n, 1, 10^7/4} ]

PARI

usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]);}
isok(k) = isprime(usigma(sigma(k))); \\ Amiram Eldar, Jan 25 2025