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.
%I A373381 #9 Jun 06 2024 08:23:33 %S A373381 0,1,1,2,1,1,1,3,2,2,1,1,1,1,1,4,1,1,1,1,2,2,1,1,2,1,3,3,1,3,1,5,1,2, %T A373381 1,2,1,1,2,2,1,1,1,1,1,2,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,2,1,6,1,1,1,3, %U A373381 1,1,1,1,1,1,1,1,1,3,1,1,4,2,1,4,2,1,2,4,1,4,2,1,1,2,1,1,1,3,3,4,1,1,1,1,3 %N A373381 a(n) = gcd(bigomega(n), A056239(n)), where bigomega is number of prime factors with repetition, and A056239 is fully additive with a(p) = primepi(p). %C A373381 As A001222 and A056239 are both fully additive sequences, all sequences that give the positions of multiples of some natural number k in this sequence are closed under multiplication, i.e., are multiplicative semigroups; for example A340784. %H A373381 Antti Karttunen, <a href="/A373381/b373381.txt">Table of n, a(n) for n = 1..100000</a> %F A373381 a(n) = gcd(A001222(n), A056239(n)). %o A373381 (PARI) %o A373381 A056239(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); %o A373381 A373381(n) = gcd(bigomega(n), A056239(n)); %Y A373381 Cf. A001222, A056239, A340784 (positions of even terms), A353331 (their characteristic function). %Y A373381 Cf. also A354871, A373370. %K A373381 nonn %O A373381 1,4 %A A373381 _Antti Karttunen_, Jun 06 2024