A346098 -id:A346098 - cp's OEIS frontend

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

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)))).

A346090 Numbers k such that k and A346098(k) are relatively prime; positions of ones in A346099, positions of zeros in A346100.

Original entry on oeis.org

1, 8, 9, 16, 18, 25, 36, 40, 42, 45, 48, 49, 50, 60, 63, 70, 77, 80, 81, 84, 90, 91, 96, 98, 100, 115, 117, 119, 120, 125, 126, 128, 133, 135, 140, 144, 147, 150, 154, 160, 161, 162, 165, 168, 169, 170, 180, 192, 195, 196, 209, 220, 221, 228, 230, 234, 238, 242, 250, 255, 256, 259, 260, 266, 270, 273, 288, 294, 297, 308, 315

Offset: 1

Antti Karttunen, Jul 07 2021

nonn

Positions of ones in A346099, positions of zeros in A346100.

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

Original entry on oeis.org

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).

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

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

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A346090 Numbers k such that k and A346098(k) are relatively prime; positions of ones in A346099, positions of zeros in A346100.

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

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Author

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PARI

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula

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

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Author

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Crossrefs

Programs

PARI

Formula