A329042 -id:A329042 - cp's OEIS frontend

A329036 Number of common divisors of n and A122111(n).

1, 2, 1, 1, 1, 4, 1, 1, 3, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 6, 2, 2, 1, 2, 1, 2, 1, 3, 1, 8, 1, 1, 2, 2, 1, 2, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 1, 2, 1, 2, 2, 3, 1, 1, 1, 8, 2, 2, 1, 4, 1, 2, 1, 1, 1, 4, 1, 3, 2, 4, 1, 2, 1, 2, 6, 3, 1, 4, 1, 3, 1, 2, 1, 12, 1, 2, 2, 4, 1, 4, 1, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 4, 1, 4, 4

Offset: 1

Antti Karttunen, Nov 08 2019

nonn

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

Cf. A000005, A001222, A122111, A280491, A329042, A329043.

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)));
A280491(n) = gcd(n,A122111(n));
A329036(n) = numdiv(A280491(n));

a(n) = A000005(A280491(n)) = A000005(gcd(n, A122111(n))).

a(n) = 1+A001222(A329042(n)) = 1+A001222(A329043(n)).

A329043 a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the exponent of the highest power of d dividing n.

Original entry on oeis.org

1, 2, 1, 1, 1, 8, 1, 1, 6, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 48, 2, 2, 1, 5, 1, 2, 1, 6, 1, 128, 1, 1, 2, 2, 1, 3, 1, 2, 2, 10, 1, 8, 1, 6, 2, 2, 1, 7, 1, 3, 2, 6, 1, 1, 1, 320, 2, 2, 1, 12, 1, 2, 1, 1, 1, 8, 1, 6, 2, 8, 1, 3, 1, 2, 48, 6, 1, 8, 1, 21, 1, 2, 1, 3072, 1, 2, 2, 20, 1, 8, 1, 6, 2, 2, 1, 11, 1, 1, 1, 1, 1, 8, 1, 20, 8

Offset: 1

Antti Karttunen, Nov 08 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A001222, A008578, A122111, A286561, A329036, A329042.

Cf. also A327167.

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)));
A329043(n) = { my(m=1,v); fordiv(A122111(n),d,if((d>1) && ((v = valuation(n,d))>0), m *= prime(v))); (m); };

a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)).

1+A001222(a(n)) = A329036(n).

cp's OEIS Frontend

A329036 Number of common divisors of n and A122111(n).

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