A305818 -id:A305818 - cp's OEIS frontend

A305983 Filter sequence combining from all proper divisors d of n, the prime signature of 2d+1.

1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 7, 4, 8, 2, 9, 2, 10, 7, 4, 2, 11, 3, 12, 4, 10, 2, 13, 2, 10, 4, 7, 7, 14, 2, 7, 12, 15, 2, 13, 2, 16, 9, 4, 2, 17, 18, 19, 7, 20, 2, 13, 4, 21, 7, 4, 2, 22, 2, 23, 24, 25, 12, 26, 2, 27, 4, 28, 2, 29, 2, 23, 24, 27, 7, 30, 2, 31, 32, 4, 2, 33, 7, 7, 4, 34, 2, 35, 36, 10, 23, 7, 7, 37, 2, 38, 9, 39, 2, 28, 2, 40, 13

Offset: 1

Antti Karttunen, Jun 15 2018

nonn

Restricted growth sequence transform of A305982.

For all i, j: a(i) = a(j) => A305818(i) = A305818(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A305973, A305982, A305985.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A305982(n) = { my(m=1); fordiv(n, d, if((dA305973(1+d)-1))); (m); }; \\ Needs also code from A305973.
v305983 = rgs_transform(vector(up_to,n,A305982(n)));
A305983(n) = v305983[n];

A086668 Number of divisors d of n such that 2d+1 is a prime.

Original entry on oeis.org

1, 2, 2, 2, 2, 4, 1, 3, 3, 3, 2, 4, 1, 3, 4, 3, 1, 6, 1, 4, 3, 3, 2, 5, 2, 3, 3, 3, 2, 7, 1, 3, 4, 2, 3, 7, 1, 2, 3, 5, 2, 6, 1, 4, 5, 3, 1, 6, 1, 4, 3, 3, 2, 7, 3, 5, 2, 3, 1, 8, 1, 2, 5, 3, 3, 6, 1, 3, 4, 5, 1, 8, 1, 3, 5, 2, 2, 7, 1, 5, 4, 3, 2, 6, 2, 3, 3, 5, 2, 10, 1, 3, 2, 2, 3, 7, 1, 4, 6, 5

Offset: 1

Jon Perry, Jul 27 2003

nonn

From Antti Karttunen, Jun 15 2018: (Start)
Number of terms of A005097 that divide n.
For all n >= 1, a(n) > A156660(n). Specifically, a(p) = 2 for all p in A005384 (Sophie Germain primes), although 2's occur in other positions as well.
(End)

			10 has divisors 1,2,5 and 10 of which 2.1+1, 2.2+1 and 2.5+1 are prime, so a(10)=3

Antti Karttunen, Table of n, a(n) for n = 1..65537

One less than A046886.

Cf. A005097, A005384, A101264, A305818.

Table[Count[Divisors[n],?(PrimeQ[2#+1]&)],{n,100}] (* _Harvey P. Dale, Apr 29 2015 *)

for (n=2,100,s=0; fordiv(i=n,i,s+=isprime(2*i+1)); print1(","s))

A086668(n) = sumdiv(n,d,isprime(d+d+1)); \\ Antti Karttunen, Jun 15 2018

From Antti Karttunen, Jun 15 2018: (Start)
a(n) = Sum_{d|n} A101264(d).
a(n) = A305818(n) + A101264(n).
(End)

Definition modified by Harvey P. Dale, Apr 29 2015

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A305983 Filter sequence combining from all proper divisors d of n, the prime signature of 2d+1.

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A086668 Number of divisors d of n such that 2d+1 is a prime.

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