A126795 -id:A126795 - cp's OEIS frontend

A325381 Lexicographically earliest sequence such that a(i) = a(j) => A048250(i) = A048250(j) and A126795(i) = A126795(j) for all i, j.

1, 2, 3, 2, 4, 5, 6, 2, 3, 7, 8, 9, 10, 11, 12, 2, 13, 5, 14, 7, 15, 16, 17, 9, 4, 18, 3, 19, 20, 21, 15, 2, 22, 23, 24, 9, 25, 26, 27, 7, 28, 29, 30, 31, 12, 32, 24, 9, 6, 7, 33, 18, 34, 5, 35, 36, 37, 38, 39, 40, 41, 42, 15, 2, 43, 44, 45, 23, 46, 47, 35, 9, 48, 49, 12, 50, 51, 52, 37, 7, 3, 53, 43, 54, 55, 56, 57, 31, 58, 59, 60, 61, 62, 47, 63, 9, 64, 11

Offset: 1

Antti Karttunen, May 08 2019

Restricted growth sequence transform of the ordered pair [A048250(n), A126795(n)].

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A048250, A126795, A291751, A325382, A325383.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A126795(n) = gcd(n,A048250(n));
v325381 = rgs_transform(vector(up_to,n,[A048250(n),A126795(n)]));
A325381(n) = v325381[n];

A325382 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = [A048250(n), A126795(n)] for all other numbers, except f(p) = -(p mod 2) for primes.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 4, 6, 7, 3, 8, 3, 9, 10, 4, 3, 5, 3, 7, 11, 12, 3, 8, 13, 14, 6, 15, 3, 16, 3, 4, 17, 18, 19, 8, 3, 20, 21, 7, 3, 22, 3, 23, 10, 24, 3, 8, 25, 7, 26, 14, 3, 5, 27, 28, 29, 30, 3, 31, 3, 32, 11, 4, 33, 34, 3, 18, 35, 36, 3, 8, 3, 37, 10, 38, 39, 40, 3, 7, 6, 41, 3, 42, 43, 44, 45, 23, 3, 46, 47, 48, 49, 36, 50, 8, 3, 9, 17, 7, 3, 51, 3, 14

Offset: 1

Antti Karttunen, May 08 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A048250, A126795, A305801, A325381, A325384.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A126795(n) = gcd(n,A048250(n));
Aux325382(n) = if(isprime(n),-(n%2),[A048250(n),A126795(n)]);
v325382 = rgs_transform(vector(up_to,n,Aux325382(n)));
A325382(n) = v325382[n];

A325385 a(n) = gcd(n-A048250(n), n-A162296(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 1, 1, 5, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 12, 19, 2, 1, 4, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 2, 1, 6, 1, 4, 3, 2, 1, 4, 41, 1, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 3, 1, 2, 1, 4, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 3, 4, 1, 18, 7, 4, 1, 2, 5, 12, 1, 1, 3, 1, 1, 6, 1, 2, 3

Offset: 1

Antti Karttunen, Apr 24 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A048250, A126795, A162296, A228058, A325313, A325314, A325375.

A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A325385(n) = gcd(n-A048250(n),n-A162296(n));

a(n) = gcd(n-A048250(n), n-A162296(n)).
a(n) = gcd(A325313(n), A325314(n)).
a(A228058(n)) = A325375(n).

A325313 a(n) = A048250(n) - n, where A048250(n) is the sum of squarefree divisors of n.

Original entry on oeis.org

0, 1, 1, -1, 1, 6, 1, -5, -5, 8, 1, 0, 1, 10, 9, -13, 1, -6, 1, -2, 11, 14, 1, -12, -19, 16, -23, -4, 1, 42, 1, -29, 15, 20, 13, -24, 1, 22, 17, -22, 1, 54, 1, -8, -21, 26, 1, -36, -41, -32, 21, -10, 1, -42, 17, -32, 23, 32, 1, 12, 1, 34, -31, -61, 19, 78, 1, -14, 27, 74, 1, -60, 1, 40, -51, -16, 19, 90, 1, -62, -77, 44, 1, 12, 23, 46

Offset: 1

Antti Karttunen, Apr 21 2019

sign

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A033879, A048250, A126795, A228058, A325314, A325315, A325319, A325320.

Array[DivisorSum[#, # &, SquareFreeQ] - # &, 86] (* Michael De Vlieger, Apr 21 2019 *)

A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A325313(n) = (A048250(n) - n);

a(n) = A048250(n) - n.
a(n) = A325314(n) - A033879(n).
a(A228058(n)) = -A325319(n).

A348929 a(n) = gcd(n, A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e.

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 12, 1, 2, 3, 1, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 1, 36, 1, 2, 1, 2, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 72, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 12, 1, 2, 3, 4, 1, 18, 7, 4, 1, 2, 5, 12, 1, 2, 3, 4, 1, 6, 1, 2, 3

Offset: 1

Antti Karttunen, Nov 07 2021

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A003959, A085731, A126865, A323166, A348507, A348928, A348999 [= a(A276086(n))].

Differs from similar A126795 for the first time at n=36, where a(36) = 36, while A126795(36) = 12.

f[p_, e_] := (p + 1)^e; a[n_] := GCD[n, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Nov 07 2021 *)

A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348929(n) = gcd(n, A003959(n));

a(n) = gcd(n, A003959(n)) = gcd(n, A348507(n)) = gcd(A003959(n), A348507(n)).

cp's OEIS Frontend

A325381 Lexicographically earliest sequence such that a(i) = a(j) => A048250(i) = A048250(j) and A126795(i) = A126795(j) for all i, j.

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A325382 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = [A048250(n), A126795(n)] for all other numbers, except f(p) = -(p mod 2) for primes.

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A325385 a(n) = gcd(n-A048250(n), n-A162296(n)).

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A325313 a(n) = A048250(n) - n, where A048250(n) is the sum of squarefree divisors of n.

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A348929 a(n) = gcd(n, A003959(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e.

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