cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A322978 Number of even divisors d of 2n such that d-1 is prime.

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%I A322978 #10 Jan 04 2019 17:36:50
%S A322978 0,1,1,2,0,3,1,2,2,2,0,5,0,2,2,3,0,4,1,3,3,2,0,6,0,1,3,3,0,6,1,3,1,2,
%T A322978 1,7,1,2,1,4,0,6,0,3,4,1,0,7,2,2,2,3,0,6,1,3,3,1,0,8,0,2,4,4,0,5,0,3,
%U A322978 2,4,0,8,0,2,3,4,1,3,1,5,3,2,0,9,0,1,2,3,0,9,2,2,2,1,1,8,1,3,3,4,0,5,0,3,4
%N A322978 Number of even divisors d of 2n such that d-1 is prime.
%H A322978 Antti Karttunen, <a href="/A322978/b322978.txt">Table of n, a(n) for n = 1..15120</a>
%H A322978 Antti Karttunen, <a href="/A322978/a322978.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A322978 a(n) = A322977(2*n).
%F A322978 a(n) = Sum_{d|(2*n), d>1} A059841(d)*A010051(d-1).
%t A322978 Array[DivisorSum[2 #, 1 &, And[EvenQ@ #, PrimeQ[# - 1]] &] &, 105] (* _Michael De Vlieger_, Jan 04 2019 *)
%o A322978 (PARI) A322978(n) = sumdiv(n+n, d, (!(d%2))*isprime(d-1));
%o A322978 (PARI)
%o A322978 A322977(n) = sumdiv(n, d, (!(d%2))*isprime(d-1));
%o A322978 A322978(n) = A322977(n+n);
%Y A322978 Cf. A010051, A059841.
%Y A322978 Bisection of A322977.
%K A322978 nonn
%O A322978 1,4
%A A322978 _Antti Karttunen_, Jan 04 2019