A305792 -id:A305792 - cp's OEIS frontend

A305793 Restricted growth sequence transform of A305792, a filter sequence constructed from binary expansions of the proper divisors of n.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 15, 10, 18, 2, 19, 2, 20, 21, 7, 22, 23, 2, 15, 21, 24, 2, 25, 2, 26, 27, 28, 2, 29, 30, 31, 10, 26, 2, 32, 33, 34, 21, 28, 2, 35, 2, 36, 37, 38, 33, 39, 2, 13, 40, 41, 2, 42, 2, 43, 44, 26, 45, 46, 2, 47, 48, 43, 2, 49, 50, 51, 40, 52, 2, 53, 45, 54, 55, 56, 33, 57, 2, 58, 59

Offset: 1

Antti Karttunen, Jun 11 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A278222, A286622, A305792, A305795.

Cf. also A293215, A300833, A304103, A305813.

\\ Needs also code from A286622:
up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A305792(n) = { my(m=1); fordiv(n,d,if(dA286622(d)-1))); (m); };
v305793 = rgs_transform(vector(up_to, n, A305792(n)));
A305793(n) = v305793[n];

For all i, j:
  a(i) = a(j) => A000005(i) = A000005(j).
  a(i) = a(j) => A292257(i) = A292257(j).
  a(i) = a(j) => A305426(i) = A305426(j).
  a(i) = a(j) => A305435(i) = A305435(j).

A305794 a(n) = Product_{d|n, d>1} prime(A286622(d)-1).

Original entry on oeis.org

1, 2, 3, 4, 5, 18, 7, 8, 15, 50, 11, 108, 11, 98, 195, 16, 5, 450, 11, 500, 357, 242, 19, 648, 55, 242, 345, 1372, 19, 76050, 29, 32, 165, 50, 385, 13500, 17, 242, 627, 5000, 17, 254898, 31, 5324, 30225, 722, 37, 3888, 77, 6050, 345, 5324, 31, 238050, 2255, 19208, 627, 722, 41, 29659500, 37, 1682, 76755, 64, 275, 54450, 11, 500, 969, 296450, 19, 405000, 17

Offset: 1

Antti Karttunen, Jun 11 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A008578, A278222, A286622, A305792, A305795 (rgs-transform).

Cf. also A304104.

A305794(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(A286622(d)-1))); (m); }; \\ Needs also code from A286622.

a(n) = Product_{d|n, d>1} A008578(A286622(d)).

For all k >= 0, a(2^k) = 2^k.

A317942 a(n) = Product_{d|n, dA286378(d)-1).

Original entry on oeis.org

1, 2, 2, 4, 2, 12, 2, 8, 6, 20, 2, 72, 2, 28, 30, 16, 2, 396, 2, 200, 42, 52, 2, 432, 10, 68, 66, 392, 2, 17100, 2, 32, 78, 92, 70, 26136, 2, 116, 102, 2000, 2, 54684, 2, 1352, 6270, 148, 2, 2592, 14, 3700, 138, 2312, 2, 178596, 130, 5488, 174, 172, 2, 9747000, 2, 188, 14322, 64, 170, 322452, 2, 4232, 222, 289100, 2, 1724976, 2

Offset: 1

Antti Karttunen, Aug 12 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences related to Stern's sequences

Cf. A286378, A317943 (restricted growth sequence transform), A317944.

Cf. also A293216, A305792.

\\ Needs also code from A286378:
A317942(n) = { my(m=1); fordiv(n,d,if(dA286378(d)-1))); (m); };

a(n) = Product_{d|n, dA008578(A286378(d)).

For all k >= 0, a(2^k) = 2^k.

A305812 a(1) = 0; for n > 1, a(n) = Product_{d|n, 1 < d < n} prime(A305788(d)-1).

Original entry on oeis.org

0, 1, 1, 2, 1, 4, 1, 6, 2, 6, 1, 60, 1, 4, 6, 42, 1, 100, 1, 198, 4, 4, 1, 4620, 3, 4, 10, 60, 1, 4620, 1, 546, 4, 26, 6, 56100, 1, 4, 4, 26334, 1, 600, 1, 60, 210, 10, 1, 1381380, 2, 132, 26, 60, 1, 18700, 6, 4620, 4, 10, 1, 66625020, 1, 4, 60, 15834, 6, 1000, 1, 2418, 10, 3300, 1, 334187700, 1, 4, 84, 60, 4, 2200, 1, 14036022, 110, 4, 1

Offset: 1

Antti Karttunen, Jun 11 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences operating on GF(2)[X]-polynomials

Cf. A008578, A278233, A305788, A305813 (rgs-transform), A305814.

Cf. also A305792, A304102.

A305812(n) = if(1==n,0, my(m=1); fordiv(n,d,if((d>1)&&(dA305788(d)-1))); (m)); \\ Needs also code from A305788.

a(1) = 0; for n > 1, a(n) = Product_{d|n, dA008578(A305788(d)).

cp's OEIS Frontend

A305793 Restricted growth sequence transform of A305792, a filter sequence constructed from binary expansions of the proper divisors of n.

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A305794 a(n) = Product_{d|n, d>1} prime(A286622(d)-1).

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PARI

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A317942 a(n) = Product_{d|n, dA286378(d)-1).

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Author

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Links

Crossrefs

Programs

PARI

Formula

A305812 a(1) = 0; for n > 1, a(n) = Product_{d|n, 1 < d < n} prime(A305788(d)-1).

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Author

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PARI

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