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A348990 a(n) = n / gcd(n, A003961(n)), where A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1). 5
1, 2, 3, 4, 5, 2, 7, 8, 9, 10, 11, 4, 13, 14, 3, 16, 17, 6, 19, 20, 21, 22, 23, 8, 25, 26, 27, 28, 29, 2, 31, 32, 33, 34, 5, 4, 37, 38, 39, 40, 41, 14, 43, 44, 9, 46, 47, 16, 49, 50, 51, 52, 53, 18, 55, 56, 57, 58, 59, 4, 61, 62, 63, 64, 65, 22, 67, 68, 69, 10, 71, 8, 73, 74, 15, 76, 7, 26, 79, 80, 81, 82, 83, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Denominator of ratio A003961(n) / n. This ratio is fully multiplicative, and A348994(n) / a(n) = A319626(A003961(n)) / A319627(A003961(n)) gives it in its lowest terms.
LINKS
FORMULA
a(n) = n / A322361(n) = n / gcd(n, A003961(n)).
a(n) = A319627(A003961(n)).
For all odd numbers n, a(n) = A003961(A319627(n)).
For all n >= 1, A000035(A348990(n)) = A000035(n). [Preserves the parity]
MATHEMATICA
Array[#1/GCD[##] & @@ {#, Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &, 84] (* Michael De Vlieger, Nov 11 2021 *)
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A348990(n) = (n/gcd(n, A003961(n)));
CROSSREFS
Cf. A000035, A000961, A002110, A003961, A319626, A319627, A319630 (fixed points), A322361, A349169 (where equal to A348992).
Cf. A348994 (numerators).
Sequence in context: A145255 A344758 A053626 * A348968 A333696 A134364
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Nov 10 2021
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)