A345941 -id:A345941 - 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).

A345942 a(n) = n / gcd(n, A329044(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 3, 4, 1, 2, 1, 4, 3, 2, 1, 8, 1, 2, 9, 4, 1, 6, 1, 16, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 7, 2, 3, 4, 1, 6, 5, 8, 3, 2, 1, 12, 1, 2, 9, 16, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 16, 27, 2, 1, 12, 5, 2, 3, 8, 1, 18, 7, 4, 3, 2, 5, 32, 1, 2, 9, 20, 1, 6

Offset: 1

Antti Karttunen, Jul 03 2021

nonn

Cf. A108951, A324886, A329044, A345941, A345943.

A345942(n) = (n/gcd(n,A329044(n))); \\ Rest of program given in A329044.

a(n) = n / A345941(n).

A345943 a(n) = A329044(n) / gcd(n, A329044(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 1, 3, 5, 5, 1, 27, 1, 7, 3125, 9, 1, 25, 1, 125, 16807, 11, 1, 45, 2401, 13, 7, 343, 1, 4375, 1, 5, 161051, 17, 99648703, 5625, 1, 19, 371293, 7, 1, 11, 1, 1331, 16807, 23, 1, 125, 23030293, 144120025, 1419857, 2197, 1, 49, 224939, 823543, 2476099, 29, 1, 8575, 1, 31, 65219, 25, 396067447082177, 285311670611

Offset: 1

Antti Karttunen, Jul 04 2021

nonn

Cf. A108951, A324886, A329044, A345941, A345942.

A345943(n) = { my(u=A329044(n)); (u / gcd(n, u)); }; \\ The rest of the program given in A329044.

a(n) = A329044(n) / A345941(n) = A329044(n) / gcd(n, A329044(n)).

A346087 a(n) = min(A071178(n), A329348(n)).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 07 2021

nonn

Each term of A345941 is a power of the greatest prime factor of n, a(n) is the exponent of that term: a(n) = A100995(A345941(n)).

Values 0..5 occur for the first time at n = 1, 2, 4, 108, 324, 9375.

Cf. A006530, A100995, A071178, A324886, A329044, A329348, A345941, A346100.

A345941(n) = gcd(n,A329044(n));
A346087(n) = isprimepower(A345941(n)); \\ Rest of program given in A329044.

a(n) = min(A071178(n), A329348(n)).
a(n) = A100995(A345941(n)).
For all n >= 1, A006530(n)^a(n) = A345941(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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A345942 a(n) = n / gcd(n, A329044(n)).

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A345943 a(n) = A329044(n) / gcd(n, A329044(n)).

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A346087 a(n) = min(A071178(n), A329348(n)).

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