cp's OEIS Frontend

A318510 Completely multiplicative with a(prime(k)) = A002487(prime(k+1)).

%I A318510 #22 May 19 2023 08:04:05
%S A318510 1,2,3,4,3,6,5,8,9,6,5,12,5,10,9,16,7,18,7,12,15,10,7,24,9,10,27,20,5,
%T A318510 18,11,32,15,14,15,36,11,14,15,24,13,30,9,20,27,14,13,48,25,18,21,20,
%U A318510 11,54,15,40,21,10,9,36,11,22,45,64,15,30,13,28,21,30,15,72,13,22,27,28,25,30,19,48,81,26,17,60,21,18,15,40
%N A318510 Completely multiplicative with a(prime(k)) = A002487(prime(k+1)).
%C A318510 Provided that the conjecture given in A261179 holds, then for all n >= 1, A007814(a(n)) = A007814(n), i.e., then the sequence preserves the 2-adic valuation of n.
%H A318510 Antti Karttunen, <a href="/A318510/b318510.txt">Table of n, a(n) for n = 1..65537</a>
%H A318510 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A318510 a(n) = A318509(A003961(n)).
%o A318510 (PARI)
%o A318510 A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A318510 A318510(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = A002487(prime(1+primepi(f[i, 1])))); factorback(f); };
%o A318510 (Python)
%o A318510 from math import prod
%o A318510 from functools import reduce
%o A318510 from sympy import factorint, nextprime
%o A318510 def A318510(n): return prod(sum(reduce(lambda x,y:(x[0],x[0]+x[1]) if int(y) else (x[0]+x[1],x[1]),bin(nextprime(p))[-1:2:-1],(1,0)))**e for p, e in factorint(n).items()) # _Chai Wah Wu_, May 18 2023
%Y A318510 Cf. A002487, A003961, A318509.
%K A318510 nonn,mult,look
%O A318510 1,2
%A A318510 _Antti Karttunen_, Aug 30 2018