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A341530
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.
13
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, 360, 2, 7, 12, 2, 336, 117, 2, 12, 4, 10, 2, 288, 4, 364, 30, 24, 6, 36, 19, 3, 360, 18, 6, 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
OFFSET
1,3
FORMULA
a(n) = gcd(A341528(n), A341529(n)) = gcd(n*A003973(n), A000203(n)*A003961(n)).
a(n) = gcd(A341512(n), A341528(n)) = gcd(A341512(n), A341529(n)) = A342670(A003961(n)). - Antti Karttunen, Mar 24 2021
PROG
(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
CROSSREFS
Cf. A000203, A003961, A003973, A028982 (positions of odd terms), A341512, A341526, A341527, A341528, A341529, A342670.
Cf. A342674 (same sequence applied onto prime shift array A246278).
Sequence in context: A136156 A191657 A155796 * A141238 A094690 A010249
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 16 2021
STATUS
approved