A280489 -id:A280489 - cp's OEIS frontend

A280488 a(n) = n / A280489(n) = n / gcd(n,A241909(n)).

1, 1, 3, 4, 5, 2, 7, 8, 3, 10, 11, 12, 13, 14, 5, 16, 17, 6, 19, 4, 7, 22, 23, 24, 25, 26, 27, 28, 29, 2, 31, 32, 11, 34, 35, 36, 37, 38, 13, 40, 41, 14, 43, 44, 9, 46, 47, 48, 49, 10, 17, 52, 53, 18, 55, 8, 19, 58, 59, 12, 61, 62, 63, 64, 65, 22, 67, 68, 23, 14, 71, 72, 73, 74, 5, 76, 77, 26, 79, 80, 81, 82, 83, 12, 85, 86, 29, 88, 89, 30, 91, 92, 31

Offset: 1

Antti Karttunen, Jan 09 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A241909, A280489, A280490, A278520.

Scheme
```
(define (A280488 n) (/ n (A280489 n)))
```

a(n) = n / A280489(n).

A331595 a(n) = gcd(A122111(n), A241909(n)).

Original entry on oeis.org

1, 2, 4, 3, 8, 3, 16, 5, 3, 3, 32, 5, 64, 3, 18, 7, 128, 15, 256, 5, 18, 3, 512, 7, 3, 3, 5, 5, 1024, 15, 2048, 11, 18, 3, 18, 7, 4096, 3, 18, 7, 8192, 15, 16384, 5, 50, 3, 32768, 11, 3, 45, 18, 5, 65536, 7, 108, 7, 18, 3, 131072, 7, 262144, 3, 50, 13, 108, 15, 524288, 5, 18, 45, 1048576, 11, 2097152, 3, 15, 5, 18, 15, 4194304, 11, 7, 3

Offset: 1

Antti Karttunen, Jan 22 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from indices in prime factorization

Cf. A122111, A241909, A241916, A331596 (number of distinct prime factors), A331597, A331598, A331599, A331600.

Cf. also A280489, A280491.

Array[If[# == 1, 1, GCD @@ {Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ #], Function[t, Times @@ Prime@ Accumulate[If[Length@ t < 2, {0}, Join[{1}, ConstantArray[0, Length@ t - 2], {-1}]] + ReplacePart[t, Map[#1 -> #2 & @@ # &, #]]]]@ ConstantArray[0, Transpose[#][[1, -1]]] &[# /. {p_, e_} /; p > 0 :> {PrimePi@ p, e}]} &@ FactorInteger[#]] &, 82] (* Michael De Vlieger, Jan 24 2020, after JungHwan Min at A122111 *)

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A241909(n) = if(1==n||isprime(n),2^primepi(n),my(f=factor(n),h=1,i,m=1,p=1,k=1); while(k<=#f~, p = nextprime(1+p); i = primepi(f[k,1]); m *= p^(i-h); h = i; if(f[k,2]>1, f[k,2]--, k++)); (p*m));
A331595(n) = gcd(A122111(n), A241909(n));

a(n) = gcd(A122111(n), A241909(n)).

a(A241916(n)) = a(n).

A280491 a(n) = gcd(n,A122111(n)).

Original entry on oeis.org

1, 2, 1, 1, 1, 6, 1, 1, 9, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 20, 3, 2, 1, 2, 1, 2, 1, 4, 1, 30, 1, 1, 3, 2, 1, 3, 1, 2, 3, 4, 1, 6, 1, 4, 5, 2, 1, 2, 1, 5, 3, 4, 1, 1, 1, 56, 3, 2, 1, 6, 1, 2, 1, 1, 1, 6, 1, 4, 3, 10, 1, 3, 1, 2, 75, 4, 1, 6, 1, 4, 1, 2, 1, 84, 1, 2, 3, 8, 1, 10, 1, 4, 3, 2, 1, 2, 1, 1, 1, 1, 1, 6, 1, 8, 15, 2, 1, 1, 1, 10, 3, 8, 1, 6, 1, 4, 1, 2

Offset: 1

Antti Karttunen, Jan 09 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A122111, A280490, also A280489.

Cf. A088902 (the fixed points, n for which a(n) = n).

(definec (A280491 n) (gcd n (A122111 n)))

a(n) = gcd(n,A122111(n)).
a(n) = n / A280490(n).
Other identities. For all n >= 1:
a(A122111(n)) = a(n).

cp's OEIS Frontend

A280488 a(n) = n / A280489(n) = n / gcd(n,A241909(n)).

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A331595 a(n) = gcd(A122111(n), A241909(n)).

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Formula

A280491 a(n) = gcd(n,A122111(n)).

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