A348990 - OEIS

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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).

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

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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

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

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)