A341530 - OEIS

%I #15 Mar 29 2021 15:04:46

%S 1,1,2,1,2,36,4,5,1,2,2,36,2,24,120,1,2,9,4,2,8,4,6,180,1,18,4,168,2,

%T 360,2,7,12,2,336,117,2,12,4,10,2,288,4,364,30,24,6,36,19,3,360,18,6,

%U 72,56,120,16,2,2,360,2,16,4,1,12,144,4,2,60,336,2,45,2,6,10,12,264,72,4,2,11,2,6,2016,4,12,24

%N a(n) = gcd(n*sigma(A003961(n)), sigma(n)*A003961(n)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors of n.

%H Antti Karttunen, <a href="/A341530/b341530.txt">Table of n, a(n) for n = 1..8191</a>

%H Antti Karttunen, <a href="/A341530/a341530.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = gcd(A341528(n), A341529(n)) = gcd(n*A003973(n), A000203(n)*A003961(n)).

%F a(n) = gcd(A341512(n), A341528(n)) = gcd(A341512(n), A341529(n)) = A342670(A003961(n)). - _Antti Karttunen_, Mar 24 2021

%o (PARI)

%o A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961

%o A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };

%Y Cf. A000203, A003961, A003973, A028982 (positions of odd terms), A341512, A341526, A341527, A341528, A341529, A342670.

%Y Cf. A342674 (same sequence applied onto prime shift array A246278).

%K nonn

%O 1,3

%A _Antti Karttunen_, Feb 16 2021