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A284203 Number of twin prime (A001097) divisors of n. 1
0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 1, 2, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 0, 0, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 0, 2, 2, 0, 1, 1, 2, 1, 1, 1, 0, 2, 1, 2, 2, 0, 1, 1, 1, 0, 2, 2, 1, 2, 1, 0, 2, 2, 0, 2, 0, 2, 1, 0, 1, 2, 1, 1, 2, 1, 1, 3, 0, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,15

LINKS

Table of n, a(n) for n=1..110.

Eric Weisstein's World of Mathematics, Twin Primes

FORMULA

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

a(A062729(n)) = 0. - Ilya Gutkovskiy, Apr 02 2017

EXAMPLE

--------------------------------------------

| n | divisors of n | twin prime    | a(n) |

|   |               | divisors of n |      |

|------------------------------------------

| 1 | {1}           |      {-}      |  0   |

| 2 | (1, 2}        |      {-)      |  0   |

| 3 | {1, 3}        |      {3}      |  1   |

| 4 | {1, 2, 4}     |      {-}      |  0   |

| 5 | {1, 5}        |      {5}      |  1   |

| 6 | {1, 2, 3, 6}  |      {3}      |  1   |

| 7 | {1, 7}        |      {7}      |  1   |

| 8 | {1, 2, 4, 8}  |      {-}      |  0   |

| 9 | {1, 3, 9}     |      {3}      |  1   |

--------------------------------------------

MATHEMATICA

nmax = 110; Rest[CoefficientList[Series[Sum[Boole[PrimeQ[k] && (PrimeQ[k - 2] || PrimeQ[k + 2])] x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]]

Table[Length[Select[Divisors[n], PrimeQ[#] && (PrimeQ[# - 2] || PrimeQ[# + 2]) &]], {n, 110}]

PROG

(PARI) concat([0, 0], Vec(sum(k=1, 110, (isprime(k) && (isprime(k - 2) || isprime(k + 2)))* x^k/(1 - x^k)) + O(x^111))) \\ Indranil Ghosh, Mar 22 2017

(Python) print [len([i for i in divisors(n) if isprime(i) and (isprime(i - 2) or isprime(i + 2))]) for n in xrange(1, 111)] # Indranil Ghosh, Mar 22 2017

CROSSREFS

Cf. A001097, A001221, A005087, A062729, A284599.

Sequence in context: A115861 A282355 A199322 * A005087 A050332 A216658

Adjacent sequences:  A284200 A284201 A284202 * A284204 A284205 A284206

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 22 2017

STATUS

approved

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Last modified February 20 01:06 EST 2018. Contains 299357 sequences. (Running on oeis4.)