

A259932


Primes whose antidivisors sum to a prime.


1



3, 5, 13, 41, 113, 761, 1201, 1741, 1861, 2113, 9661, 9941, 12641, 13613, 15313, 21841, 23981, 30013, 34061, 47741, 49613, 60901, 70313, 83641, 101701, 237361, 241513, 252761, 303421, 335381, 377581, 413141, 489061, 491041, 525313, 529421, 637321, 695021, 718801
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OFFSET

1,1


COMMENTS

See A066272 for definition of antidivisor.
Subsequence of A109350.
Apparently, apart from 5, all terms are congruent to {1, 3} mod 5 (see A045429).


LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..100


EXAMPLE

The antidivisor of 3 is 2, which is prime.
The antidivisors of 41 are 2, 3, 9, and 27, whose sum is 41, which is prime.
The antidivisors of 9941 are 2, 3, 9, 47, 59, 141, 337, 423, 2209, and 6627, whose sum is 9857, which is prime.


MAPLE

with(numtheory): P:=proc(q) local a, i, j, n;
for n from 3 to q do if isprime(n) then
i:=0; j:=n; while j mod 2 <> 1 do i:=i+1; j:=j/2; od;
if isprime(sigma(2*n+1)+sigma(2*n1)+sigma(n/2^i)*2^(i+1)6*n2)
then print(n); fi; fi; od; end: P(10^9);


MATHEMATICA

ad[n_] := Cases[Range[2, n  1], _?(Abs[Mod[n, #]  #/2] < 1 &)]; Select[Prime@ Range@ 1250, PrimeQ[Total@ ad@ #] &] (* Michael De Vlieger, Jul 10 2015 *)


CROSSREFS

Cf. A000040, A045429, A066272, A066417, A109350.
Sequence in context: A172023 A271667 A188583 * A178432 A236068 A057188
Adjacent sequences: A259929 A259930 A259931 * A259933 A259934 A259935


KEYWORD

nonn


AUTHOR

Paolo P. Lava, Jul 09 2015


STATUS

approved



