A284599 Sum of twin prime (A001097) divisors of n.

0, 0, 3, 0, 5, 3, 7, 0, 3, 5, 11, 3, 13, 7, 8, 0, 17, 3, 19, 5, 10, 11, 0, 3, 5, 13, 3, 7, 29, 8, 31, 0, 14, 17, 12, 3, 0, 19, 16, 5, 41, 10, 43, 11, 8, 0, 0, 3, 7, 5, 20, 13, 0, 3, 16, 7, 22, 29, 59, 8, 61, 31, 10, 0, 18, 14, 0, 17, 3, 12, 71, 3, 73, 0, 8, 19, 18, 16, 0, 5, 3, 41, 0, 10, 22, 43, 32, 11, 0, 8

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Primes

Index entries for sequences related to sums of divisors

Formula

G.f.: Sum_{k>=1} A001097(k)*x^A001097(k)/(1 - x^A001097(k)).

a(n) = Sum_{d|n, d twin prime} d.

a(A062729(n)) = 0.

a(A001097(n)) = A001097(n).

Example

a(15) = 8 because 15 has 4 divisors {1, 3, 5, 15} among which 2 are twin primes {3, 5} therefore 3 + 5 = 8.

Maple

N:= 200: # to get a(1)..a(N)
P:= select(isprime, {seq(i, i=3..N+2)}):
TP:= P intersect map(`-`, P, 2):
TP:= TP union map(`+`, TP, 2):
V:= Vector(N):
for p in TP do
  pm:= [seq(i, i=p..N, p)];
  V[pm]:= map(`+`, V[pm], p);
od:
convert(V, list); # Robert Israel, Mar 30 2017

Mathematica

Table[Total[Select[Divisors[n], PrimeQ[#1] && (PrimeQ[#1 - 2] || PrimeQ[#1 + 2]) &]], {n, 80}]

Prog

(Python)
from sympy import divisors, isprime
def a(n): return sum([i for i in divisors(n) if isprime(i) and (isprime(i - 2) or isprime(i + 2))])
print([a(n) for n in range(1, 91)]) # Indranil Ghosh, Mar 30 2017
(PARI) a(n) = sumdiv(n, d, d*(isprime(d) && (isprime(d-2) || isprime(d+2)))); \\ Michel Marcus, Apr 02 2017

Crossrefs

Cf. A001097, A008472, A062729, A284203.

Sequence in context: A336597 A076109 A078788 * A005069 A366840 A284233

Adjacent sequences: A284596 A284597 A284598 * A284600 A284601 A284602

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 30 2017

Status

approved