A348994 a(n) = A003961(n) / gcd(n, A003961(n)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1).

1, 3, 5, 9, 7, 5, 11, 27, 25, 21, 13, 15, 17, 33, 7, 81, 19, 25, 23, 63, 55, 39, 29, 45, 49, 51, 125, 99, 31, 7, 37, 243, 65, 57, 11, 25, 41, 69, 85, 189, 43, 55, 47, 117, 35, 87, 53, 135, 121, 147, 95, 153, 59, 125, 91, 297, 115, 93, 61, 21, 67, 111, 275, 729, 119, 65, 71, 171, 145, 33, 73, 75, 79, 123, 49, 207

Offset

1,2

Comments

Numerator of ratio A003961(n) / n. This ratio is fully multiplicative, and a(n) / A348990(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) = A003961(n) / gcd(n, A003961(n)).

a(n) = A319626(A003961(n)).

Mathematica

Array[#2/GCD[##] & @@ {#, If[# == 1, 1, Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]]} &, 76] (* 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); };
A348994(n) = (A003961(n) / gcd(n, A003961(n)));

Crossrefs

Cf. A003961, A319626, A319627, A348990 (denominators).

Sequence in context: A021282 A016613 A336849 * A079427 A168271 A081761

Adjacent sequences: A348991 A348992 A348993 * A348995 A348996 A348997

Keyword

nonn,frac

Author

Antti Karttunen, Nov 10 2021

Status

approved