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A259932 Primes whose anti-divisors 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A066272 for definition of anti-divisor.

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 anti-divisor of 3 is 2, which is prime.

The anti-divisors of 41 are 2, 3, 9, and 27, whose sum is 41, which is prime.

The anti-divisors 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*n-1)+sigma(n/2^i)*2^(i+1)-6*n-2)

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

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Last modified October 16 19:00 EDT 2018. Contains 316271 sequences. (Running on oeis4.)