cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A280498 a(n) = A032742(A249818(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 10, 9, 11, 1, 12, 5, 13, 7, 14, 1, 15, 1, 16, 15, 17, 7, 18, 1, 19, 11, 20, 1, 21, 1, 22, 27, 23, 1, 24, 7, 25, 25, 26, 1, 27, 25, 28, 21, 29, 1, 30, 1, 31, 13, 32, 11, 33, 1, 34, 45, 35, 1, 36, 1, 37, 17, 38, 11, 39, 1, 40, 33, 41, 1, 42, 35, 43, 35, 44, 1, 45, 49, 46, 81, 47, 13, 48, 1, 49, 19, 50, 1
Offset: 1

Views

Author

Antti Karttunen, Jan 09 2017

Keywords

Links

Crossrefs

Cf. A020639, A032742, A249818.
Differs from related A280495 and A280497 for the first time at n=33, where a(33) = 15, while A280495(33) = A280497(33) = 13.
Differs from related A280496 for the first time at n=42, where a(42) = 21, while A280496(42) = 27.

Programs

Formula

a(n) = A032742(A249818(n)).
a(n) = A249818(n) / A020639(n). [Because A249818 preserves the smallest prime factor of n.]

A280692 a(n) = A003961(n) - A250469(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 6, 0, -6, 0, 12, 0, -6, 0, 36, 0, 24, 0, 6, 0, -24, 0, 66, 0, -24, 60, 18, 0, 18, 0, 150, -20, -42, 0, 120, 0, -42, -10, 72, 0, 42, 0, -12, 60, -48, 0, 264, 0, 0, -30, 0, 0, 216, 0, 132, -30, -78, 0, 138, 0, -72, 120, 540, 0, 0, 0, -30, -30, 24, 0, 462, 0, -96, 60, -18, 0, 24, 0, 330, 420, -114, 0, 246
Offset: 1

Views

Author

Antti Karttunen, Mar 08 2017

Keywords

Links

Crossrefs

Cf. A003961, A250469, A249820, A280492, A280497, A280498, A280702.
Cf. A280693 (gives the positions of zeros).
Cf. also arrays A083221 and A246278.

Programs

  • Mathematica
    f[n_] := f[n] = Which[n == 1, 1, PrimeQ@ n, NextPrime@ n, True, Times @@ Replace[FactorInteger[n], {p_, e_} :> f[p]^e, 1]]; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[ Function[{m, n}, f@ n - Lookup[s, g[n] + 1][[m]] + Boole[n == 1]][#1, First@ #2] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* Michael De Vlieger, Mar 09 2017, Version 10 *)
  • Scheme
    (define (A280692 n) (- (A003961 n) (A250469 n)))

Formula

a(n) = A003961(n) - A250469(n).

A280496 a(n) = A032742(A250246(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 10, 9, 11, 1, 12, 5, 13, 7, 14, 1, 15, 1, 16, 15, 17, 7, 18, 1, 19, 11, 20, 1, 27, 1, 22, 27, 23, 1, 24, 7, 25, 25, 26, 1, 21, 25, 28, 21, 29, 1, 30, 1, 31, 13, 32, 11, 45, 1, 34, 45, 35, 1, 36, 1, 37, 17, 38, 11, 33, 1, 40, 33, 41, 1, 54, 35, 43, 35, 44, 1, 81, 49, 46, 81, 47, 13, 48, 1, 49, 19, 50, 1
Offset: 1

Views

Author

Antti Karttunen, Jan 09 2017

Keywords

Links

Crossrefs

Cf. A020639, A032742, A250246.
Differs from related A280495 and A280497 for the first time at n=33, where a(33) = 15, while A280495(33) = A280497(33) = 13.
Differs from related A280498 for the first time at n=42, where a(42) = 27, while A280498(42) = 21.

Programs

Formula

a(n) = A032742(A250246(n)).
a(n) = A250246(n) / A020639(n). [Because A250246 preserves the smallest prime factor of n.]

A280702 a(n) = gcd(A003961(n), A250469(n)).

Original entry on oeis.org

1, 3, 5, 9, 7, 15, 11, 3, 25, 3, 13, 3, 17, 3, 35, 9, 19, 3, 23, 3, 55, 3, 29, 3, 49, 3, 5, 9, 31, 3, 37, 3, 5, 3, 77, 15, 41, 3, 5, 9, 43, 3, 47, 3, 5, 3, 53, 3, 121, 147, 5, 153, 59, 3, 91, 33, 5, 3, 61, 3, 67, 3, 5, 27, 119, 195, 71, 3, 5, 3, 73, 3, 79, 3, 5, 9, 143, 3, 83, 3, 5, 3, 89, 3, 133, 3, 5, 9, 97, 3, 187, 3, 5, 3, 161
Offset: 1

Views

Author

Antti Karttunen, Mar 08 2017

Keywords

Comments

For n > 1, a(n) > 1 because A020639(A003961(n)) = A020639(A250469(n)) = A003961(A020639(n)).

Links

Crossrefs

Cf. A003961, A020639, A250469, A280497, A280498, A280692, A280703, A280704, A283463, A283464.

Programs

  • Mathematica
    f[n_] := f[n] = Which[n == 1, 1, PrimeQ@ n, NextPrime@ n, True, Times @@ Replace[FactorInteger[n], {p_, e_} :> f[p]^e, 1]]; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[ GCD[ Lookup[s, g[First@ #2] + 1][[#1]] - Boole[First@ #2 == 1], f@ First@ #2] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* Michael De Vlieger, Mar 08 2017 *)
  • Scheme
    (define (A280702 n) (gcd (A003961 n) (A250469 n)))

Formula

a(n) = gcd(A003961(n), A250469(n)).

A280492 a(1) = 0; for n > 1, a(n) = A246277(n) - A078898(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 7, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 7, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 5, 0, 8, 0, 0, 0, 1, 0, 13, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 12, 0, 0, 0, 9, 0, 2, 0, 2
Offset: 1

Views

Author

Antti Karttunen, Jan 09 2017

Keywords

Comments

For n > 1, a(n) gives the difference of column positions of n's location in arrays A246278 and A083221. Note that any n occurs on the same row in both arrays.

Links

Crossrefs

Cf. A078898, A083221, A246277, A246278, A249820.
Cf. also A278523, A279350, A280497, A280498.

Programs

Formula

a(1) = 0; for n > 1, a(n) = A246277(n) - A078898(n).

A280495 a(n) = A032742(A250245(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 10, 9, 11, 1, 12, 5, 13, 7, 14, 1, 15, 1, 16, 13, 17, 7, 18, 1, 19, 21, 20, 1, 27, 1, 22, 11, 23, 1, 24, 7, 25, 25, 26, 1, 21, 13, 28, 33, 29, 1, 30, 1, 31, 19, 32, 19, 39, 1, 34, 37, 35, 1, 36, 1, 37, 17, 38, 11, 63, 1, 40, 15, 41, 1, 54, 31, 43, 45, 44, 1, 33, 17, 46, 57, 47, 37, 48, 1, 49, 27, 50, 1
Offset: 1

Views

Author

Antti Karttunen, Jan 09 2017

Keywords

Links

Crossrefs

Cf. A020639, A032742, A250245.
Differs from related A280496 and A280498 for the first time at n=33, where a(33) = 13, while A280496(33) = A280498(33) = 15.
Differs from related A280497 for the first time at n=42, where a(42) = 27, while A280497(42) = 21.

Programs

Formula

a(n) = A032742(A250245(n)).
a(n) = A250245(n) / A020639(n). [Because A250245 preserves the smallest prime factor of n.]

A283463 a(n) = A032742(A266645(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 5, 3, 4, 1, 7, 1, 11, 5, 6, 1, 13, 1, 17, 7, 10, 1, 19, 5, 9, 11, 8, 1, 23, 1, 29, 13, 14, 7, 15, 1, 31, 17, 22, 1, 37, 1, 41, 19, 12, 1, 43, 7, 25, 9, 26, 1, 47, 11, 21, 23, 34, 1, 53, 1, 59, 29, 20, 13, 33, 1, 61, 15, 38, 1, 67, 1, 71, 31, 18, 11, 35, 1, 73, 37, 16, 1, 79, 17, 39, 41, 46, 1, 83, 13, 55, 43, 58, 19, 51
Offset: 1

Views

Author

Antti Karttunen, Mar 08 2017

Keywords

Links

Crossrefs

Cf. A020639, A032742, A266645, A280497, A280498, A283464, A283465.

Programs

  • Mathematica
    f[n_] := Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[Function[{m, n}, If[# == 1, 1, Divisors[#][[-2]]] &@ f[Lookup[s, g[n] + 1][[m]] - Boole[n == 1]]][#1, First@ #2] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4] (* Michael De Vlieger, Mar 09 2017, Version 10 *)
  • Scheme
    (define (A283463 n) (A032742 (A266645 n)))

Formula

a(n) = A032742(A266645(n)).
a(n) = A266645(n) / A020639(n). [Because A266645 preserves the smallest prime factor of n.]

A283464 a(n) = A032742(A266646(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 5, 3, 4, 1, 8, 1, 6, 5, 14, 1, 13, 1, 11, 7, 7, 1, 23, 5, 9, 17, 17, 1, 18, 1, 41, 9, 10, 7, 38, 1, 12, 11, 32, 1, 28, 1, 20, 23, 15, 1, 68, 7, 25, 13, 26, 1, 63, 11, 50, 15, 16, 1, 53, 1, 19, 37, 122, 13, 33, 1, 29, 19, 39, 1, 113, 1, 21, 33, 35, 11, 43, 1, 95, 83, 22, 1, 83, 17, 24, 21, 59, 1, 88, 13, 44, 25, 27, 19, 203
Offset: 1

Views

Author

Antti Karttunen, Mar 08 2017

Keywords

Links

Crossrefs

Cf. A020639, A032742, A266646, A280497, A280498, A283463, A283466.

Programs

Formula

a(n) = A032742(A266646(n)).
a(n) = A266646(n) / A020639(n). [Because A266646 preserves the smallest prime factor of n.]
Showing 1-8 of 8 results.

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