A356167 -id:A356167 - cp's OEIS frontend

A356164 a(n) is the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

1, 2, 2, 4, 3, 2, 5, 8, 4, 6, 7, 4, 11, 10, 3, 16, 13, 4, 17, 12, 10, 14, 19, 8, 9, 22, 8, 20, 23, 6, 29, 32, 14, 26, 5, 4, 31, 34, 22, 24, 37, 10, 41, 28, 6, 38, 43, 16, 25, 18, 26, 44, 47, 8, 21, 40, 34, 46, 53, 12, 59, 58, 20, 64, 33, 14, 61, 52, 38, 10, 67, 8, 71, 62, 9, 68, 7, 22, 73, 48, 16, 74, 79, 20, 39, 82

Offset: 1

Antti Karttunen, Jul 28 2022

nonn

a(n) is the smallest positive k such that A191002(k) is a multiple of n.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A000040, A003961, A191002, A356165, A356166, A356167, A356168, A356169.

Cf. also A344005, A355944.

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356164(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(k)));

a(n) = n - A356165(n).

For n >= 2, a(A000040(n)) = A000040(n-1).

A356166 Greatest common divisor of n and the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

Original entry on oeis.org

1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 3, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 32, 1, 2, 5, 4, 1, 2, 1, 8, 1, 2, 1, 4, 3, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 12, 1, 2, 1, 64, 1, 2, 1, 4, 1, 10, 1, 8, 1, 2, 3, 4, 7, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 6, 1, 4, 1, 2, 1, 32, 1, 2, 1, 4, 1, 2, 1, 8, 5

Offset: 1

Antti Karttunen, Jul 28 2022

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A003961, A191002, A356164, A356165, A356167, A356168, A356171 (positions of 1's), A356172.

Cf. also A345992, A356151.

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356166(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(gcd(n,k))));

a(n) = gcd(n, A356164(n)) = gcd(n, A356165(n)) = gcd(A356164(n), A356165(n)).

A356168 Greatest common divisor of n and A003961(A356164(n)), where A356164(n) is the smallest positive k such that n divides k*A003961(k), and A003961 is fully multiplicative with a(p) = nextprime(p).

Original entry on oeis.org

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 5, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 1, 33, 17, 7, 9, 37, 19, 39, 5, 41, 21, 43, 11, 15, 23, 47, 3, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 1, 65, 33, 67, 17, 69, 7, 71, 9, 73, 37, 25, 19, 11, 39, 79, 5, 81, 41, 83, 21, 85, 43

Offset: 1

Antti Karttunen, Jul 28 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A003961, A356164, A356166, A356167, A356169.

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A356168(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(gcd(n,A003961(k)))));

a(n) = gcd(n, A003961(A356164(n))).

a(n) = gcd(n, A356169(n)) = n - A356169(n).

cp's OEIS Frontend

A356164 a(n) is the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

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A356166 Greatest common divisor of n and the smallest positive k such that n divides k*A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

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A356168 Greatest common divisor of n and A003961(A356164(n)), where A356164(n) is the smallest positive k such that n divides k*A003961(k), and A003961 is fully multiplicative with a(p) = nextprime(p).

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