A283464 -id:A283464 - cp's OEIS frontend

A280702 a(n) = gcd(A003961(n), A250469(n)).

1, 3, 5, 9, 7, 15, 11, 3, 25, 3, 13, 3, 17, 3, 35, 9, 19, 3, 23, 3, 55, 3, 29, 3, 49, 3, 5, 9, 31, 3, 37, 3, 5, 3, 77, 15, 41, 3, 5, 9, 43, 3, 47, 3, 5, 3, 53, 3, 121, 147, 5, 153, 59, 3, 91, 33, 5, 3, 61, 3, 67, 3, 5, 27, 119, 195, 71, 3, 5, 3, 73, 3, 79, 3, 5, 9, 143, 3, 83, 3, 5, 3, 89, 3, 133, 3, 5, 9, 97, 3, 187, 3, 5, 3, 161

Offset: 1

Antti Karttunen, Mar 08 2017

nonn

For n > 1, a(n) > 1 because A020639(A003961(n)) = A020639(A250469(n)) = A003961(A020639(n)).

Antti Karttunen, Table of n, a(n) for n = 1..13330

Cf. A003961, A020639, A250469, A280497, A280498, A280692, A280703, A280704, A283463, A283464.

f[n_] := f[n] = Which[n == 1, 1, PrimeQ@ n, NextPrime@ n, True, Times @@ Replace[FactorInteger[n], {p_, e_} :> f[p]^e, 1]]; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[ GCD[ Lookup[s, g[First@ #2] + 1][[#1]] - Boole[First@ #2 == 1], f@ First@ #2] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* Michael De Vlieger, Mar 08 2017 *)

(define (A280702 n) (gcd (A003961 n) (A250469 n)))

a(n) = gcd(A003961(n), A250469(n)).

A283463 a(n) = A032742(A266645(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 5, 3, 4, 1, 7, 1, 11, 5, 6, 1, 13, 1, 17, 7, 10, 1, 19, 5, 9, 11, 8, 1, 23, 1, 29, 13, 14, 7, 15, 1, 31, 17, 22, 1, 37, 1, 41, 19, 12, 1, 43, 7, 25, 9, 26, 1, 47, 11, 21, 23, 34, 1, 53, 1, 59, 29, 20, 13, 33, 1, 61, 15, 38, 1, 67, 1, 71, 31, 18, 11, 35, 1, 73, 37, 16, 1, 79, 17, 39, 41, 46, 1, 83, 13, 55, 43, 58, 19, 51

Offset: 1

Antti Karttunen, Mar 08 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001

Cf. A020639, A032742, A266645, A280497, A280498, A283464, A283465.

f[n_] := Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[Function[{m, n}, If[# == 1, 1, Divisors[#][[-2]]] &@ f[Lookup[s, g[n] + 1][[m]] - Boole[n == 1]]][#1, First@ #2] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* Michael De Vlieger, Mar 09 2017, Version 10 *)

(define (A283463 n) (A032742 (A266645 n)))

a(n) = A032742(A266645(n)).

a(n) = A266645(n) / A020639(n). [Because A266645 preserves the smallest prime factor of n.]

A283466 a(n) = A046523(A266646(n)).

Original entry on oeis.org

1, 2, 2, 4, 2, 6, 2, 6, 4, 8, 2, 16, 2, 12, 6, 12, 2, 6, 2, 6, 6, 6, 2, 6, 4, 12, 6, 6, 2, 36, 2, 6, 8, 12, 6, 12, 2, 24, 6, 64, 2, 24, 2, 24, 6, 30, 2, 24, 4, 12, 6, 12, 2, 60, 6, 36, 12, 32, 2, 6, 2, 6, 6, 12, 6, 30, 2, 6, 6, 30, 2, 6, 2, 30, 12, 30, 6, 6, 2, 30, 6, 12, 2, 6, 6, 48, 12, 6, 2, 48, 6, 24, 12, 24, 6, 30, 2, 6, 6, 12, 2, 96, 2, 30

Offset: 1

Antti Karttunen, Mar 08 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..816

Cf. A046523, A266646, A283464, A283465.

(define (A283466 n) (A046523 (A266646 n)))

a(n) = A046523(A266646(n)).

cp's OEIS Frontend

A280702 a(n) = gcd(A003961(n), A250469(n)).

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A283463 a(n) = A032742(A266645(n)).

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A283466 a(n) = A046523(A266646(n)).

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