A346095 -id:A346095 - cp's OEIS frontend

A346096 Numerator of the primorial deflation of A276086(A108951(n)): a(n) = A319626(A324886(n)).

2, 3, 5, 9, 7, 25, 11, 5, 7, 49, 13, 625, 17, 121, 117649, 25, 19, 49, 23, 2401, 1771561, 169, 29, 175, 14641, 289, 55, 14641, 31, 26411, 37, 21, 4826809, 361, 299393809, 2401, 41, 529, 24137569, 11, 43, 13, 47, 28561, 161051, 841, 53, 343, 6311981, 214358881, 47045881, 83521, 59, 3025, 48841, 214358881, 148035889, 961

Offset: 1

Antti Karttunen, Jul 07 2021

Numerator of ratio A324886(n) / A329044(n).

Cf. A346097 (denominators).
Cf. A003961, A108951, A319626, A324886, A329044, A346095, A346098, A346106, A346108.
Cf. also A337376, A345941.

A064989(n) = { my(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); };
A319626(n) = (n / gcd(n, A064989(n)));
A346096(n) = A319626(A324886(n)); \\ Rest of program in A324886.

a(n) = A319626(A324886(n)).
a(n) = A324886(n) / A346095(n) = A324886(n) / gcd(A324886(n), A329044(n)).
For n >= 1, A108951(A346096(n)) / A108951(A346097(n)) = A324886(n).
For n > 1, a(n) = A003961(A346098(n)).

A346097 Denominator of the primorial deflation of A276086(A108951(n)): a(n) = A319627(A324886(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 9, 7, 2, 3, 25, 11, 81, 13, 49, 15625, 4, 17, 9, 19, 625, 117649, 121, 23, 27, 1225, 169, 21, 2401, 29, 3125, 31, 10, 1771561, 289, 5764801, 81, 37, 361, 4826809, 5, 41, 7, 43, 14641, 12005, 529, 47, 75, 1127357, 1500625, 24137569, 28561, 53, 441, 14641, 5764801, 47045881, 841, 59, 125, 61, 961, 343, 100, 302875106592253

Offset: 1

Antti Karttunen, Jul 07 2021

Denominator of ratio A324886(n) / A329044(n).

Cf. A346096 (numerators).
Cf. A006530, A020639, A108951, A276086, A319627, A324886, A329044, A345941 [= gcd(n, a(n))], A346095, A346098, A346107, A346109.
Cf. also A337377.

A064989(n) = { my(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); };
A319627(n) = (A064989(n) / gcd(n, A064989(n)));
A346097(n) = A319627(A324886(n)); \\ Rest of program given in A324886.

a(n) = A319627(A324886(n)).
a(n) = A329044(n) / A346095(n) = A329044(n) / gcd(A324886(n), A329044(n)).
A020639(a(n)) = A006530(n).
A108951(a(n)) = A346107(n).
A346105(a(n)) = A346109(n).

A346098 a(n) = A064989(A346096(n)) = A064989(A319626(A324886(n))).

Original entry on oeis.org

1, 2, 3, 4, 5, 9, 7, 3, 5, 25, 11, 81, 13, 49, 15625, 9, 17, 25, 19, 625, 117649, 121, 23, 45, 2401, 169, 21, 2401, 29, 4375, 31, 10, 1771561, 289, 14235529, 625, 37, 361, 4826809, 7, 41, 11, 43, 14641, 16807, 529, 47, 125, 2093663, 5764801, 24137569, 28561, 53, 441, 20449, 5764801, 47045881, 841, 59, 343, 61, 961, 1331, 100, 396067447082177

Offset: 1

Antti Karttunen, Jul 07 2021

nonn

Cf. A064989, A319626, A324886, A346095, A346096, A346097, A346099 [= gcd(n, a(n))].

A064989(n) = { my(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); };
A319626(n) = (n / gcd(n, A064989(n)));
A346098(n) = A064989(A319626(A324886(n))); \\ Rest of program given in A324886.

a(n) = A064989(A346096(n)) = A064989(A319626(A324886(n))).

A346099 a(n) = gcd(n, A346098(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 3, 7, 1, 1, 5, 11, 3, 13, 7, 5, 1, 17, 1, 19, 5, 7, 11, 23, 3, 1, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 1, 37, 19, 13, 1, 41, 1, 43, 11, 1, 23, 47, 1, 1, 1, 17, 13, 53, 9, 11, 7, 19, 29, 59, 1, 61, 31, 1, 4, 13, 11, 67, 17, 23, 1, 71, 3, 73, 37, 25, 19, 1, 13, 79, 1, 1, 41, 83, 1, 17, 43, 29, 11, 89

Offset: 1

Antti Karttunen, Jul 07 2021

nonn

Only powers of primes (A000961) occur as terms. A346100 lists the exponents.

Cf. A000961, A064989, A319626, A324886, A346095, A346096, A346097, A346098, A346100.

Cf. A346090 (positions of ones).

A064989(n) = { my(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); };
A319626(n) = (n / gcd(n, A064989(n)));
A346099(n) = gcd(n, A064989(A319626(A324886(n)))); \\ Rest of program in A324886.

a(n) = gcd(n, A346098(n)) = gcd(n, A064989(A319626(A324886(n)))).

A346100 a(n) = A100995(gcd(n, A064989(A319626(A324886(n))))).

Original entry on oeis.org

0, 1, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 3

Offset: 1

Antti Karttunen, Jul 07 2021

nonn

Cf. A064989, A100995, A319626, A324886, A346087, A346095, A346096, A346098, A346099.

Cf. A346090 (positions of 0's).

A064989(n) = { my(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); };
A319626(n) = (n / gcd(n, A064989(n)));
A346100(n) = isprimepower(gcd(n, A064989(A319626(A324886(n))))); \\ Rest of program given in A324886.

a(n) = A100995(A346099(n)) = A100995(gcd(n, A064989(A319626(A324886(n))))).

cp's OEIS Frontend

A346096 Numerator of the primorial deflation of A276086(A108951(n)): a(n) = A319626(A324886(n)).

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A346097 Denominator of the primorial deflation of A276086(A108951(n)): a(n) = A319627(A324886(n)).

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A346098 a(n) = A064989(A346096(n)) = A064989(A319626(A324886(n))).

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A346099 a(n) = gcd(n, A346098(n)).

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A346100 a(n) = A100995(gcd(n, A064989(A319626(A324886(n))))).

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