A343418 Primes that occur in A343416.

11, 29, 41, 61, 73, 97, 131, 137, 139, 149, 151, 157, 167, 179, 191, 211, 227, 229, 233, 241, 251, 283, 293, 307, 313, 331, 347, 373, 383, 389, 397, 401, 449, 463, 521, 577, 607, 631, 641, 647, 653, 661, 673, 677, 701, 709, 719, 727, 757, 769, 811, 821, 823, 829, 857, 859, 877, 887, 907, 919, 929

Offset

1,1

Comments

Terms are distinct and in numerical order, not the order they occur in A343416.

If p, 6*p-1 and 19*p+4 are prime, then 19*p+4 = A343416(6*p-1) is a term. Dickson's conjecture implies that there are infinitely many such terms.

Links

Robert Israel, Table of n, a(n) for n = 1..4000

Example

a(3) = 41 is a term because 41 = A343416(8) = A343416(10) and is prime.

Maple

spf:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
f:= proc(n) local a, b;
  a:= spf(n);
  b:= numtheory:-sigma(n);
  a+b+spf(b)+numtheory:-sigma(a)
end proc:
S:= select(t -> t < 1000 and isprime(t), map(f, {$1..1000})):
sort(convert(S, list));

Crossrefs

Cf. A343416.

Sequence in context: A240678 A087693 A106017 * A106065 A247089 A156110

Adjacent sequences: A343415 A343416 A343417 * A343419 A343420 A343421

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 14 2021

Status

approved