A129995 -id:A129995 - cp's OEIS frontend

A131192 Numbers n >= 0 such that d(n) = (n^1 + 1)(n^2 + 2)...*(n^26 + 26) / 26! is nonintegral.

7, 11, 18, 24, 29, 37, 40, 50, 51, 62, 73, 76, 84, 89, 95, 102, 106, 115, 128, 139, 141, 150, 154, 161, 167, 172, 180, 183, 193, 194, 205, 206, 216, 219, 227, 245, 249, 258, 260, 271, 282, 284, 293, 297, 304, 310, 315, 323, 326, 336, 337, 348, 349, 362, 370, 375, 381, 388, 392, 403, 414, 425, 427, 436

Offset: 1

Alexander R. Povolotsky, Sep 25 2007

nonn

Notice that 26! = 2^23 * 3^10 * 5^6 * 7^3 * 11^2 * 13^2 * 17 * 19 * 23. There is no divisibility for 11^2 and n in {11m+7} \ {121m+117} and for 13^2 and n in {13m+11} \ {169m+63}. Therefore, this sequence is formed by the union ( {11m+7} \ {121m+117} ) U ( {13m+11} \ {169m+63}). - Max Alekseyev, Nov 10 2007

Cf. A129995, A131189, A131190, A131191, A131685.

d:=proc(n) options operator, arrow: (product(n^j+j,j=1..26))/factorial(26) end proc: a:=proc(n) if type(d(n), integer) = false then n else end if end proc; seq(a(n),n=1..300); # Emeric Deutsch, Oct 24 2007

Initial terms were calculated by Peter J. C. Moses; see comment in A129995
More terms from Emeric Deutsch, Oct 24 2007
More terms from Max Alekseyev, Feb 02 2015

A131677 a(n) = (Product_{i=1..7} n^i+i) / 7!.

Original entry on oeis.org

1, 8, 274725, 8903032600, 21521701559085, 9892478959203456, 1527238784041075105, 109733832449349303000, 4483781212288588835625, 118795734924428077310080, 2233888850312257843810061, 31811523551546985038211552, 359951182400070234774044725

Offset: 0

Alexander R. Povolotsky, Sep 15 2007

See A131685 about well-definedness. - M. F. Hasler, May 02 2015

G. C. Greubel, Table of n, a(n) for n = 0..1000

Table[Product[ n^i + i, {i, 1, 7}]/7!, {n, 0, 12}] (* Michael De Vlieger, Jan 03 2016 *)

A131677(n,k=7)=prod(i=1,k,(n^i+i))/k! \\ Changing the optional 2nd argument allows one to produce A000027 (k=1), A064808 (k=2), A131509 (k=3), A129995 (k=4), A131675 (k=5), ..., A131680 (k=10). - M. F. Hasler, May 02 2015

Definition made explicit by M. F. Hasler, May 02 2015

A131678 a(n) = (Product_{i=1..8} n^i+i) / 8!.

Original entry on oeis.org

1, 9, 9065925, 7310502643675, 176327300873583405, 483041091658815453456, 320648364425775841520065, 79074323113562613259765875, 9403175220694650942397475625, 639220975955961365494757841040, 27923612862792073359883606310061, 852385355738368243011331354210716, 19346552845649626158477975728463925

Offset: 0

Alexander R. Povolotsky, Sep 15 2007

nonn

See A131685 about well-definedness. - M. F. Hasler, May 02 2015

G. C. Greubel, Table of n, a(n) for n = 0..1000

Table[Product[ n^i + i, {i, 1, 8}]/8!, {n, 0, 12}] (* Michael De Vlieger, Jan 03 2016 *)

A131678(n,k=8)=prod(i=1,k,(n^i+i))/k! \\ Changing the optional 2nd argument allows one to produce A000027 (k=1), A064808 (k=2), A131509 (k=3), A129995(k=4), A131675 (k=5), ..., A131680 (k=10). - M. F. Hasler, May 02 2015

Definition made explicit by M. F. Hasler, May 02 2015

cp's OEIS Frontend

A131192 Numbers n >= 0 such that d(n) = (n^1 + 1)(n^2 + 2)...*(n^26 + 26) / 26! is nonintegral.

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A131677 a(n) = (Product_{i=1..7} n^i+i) / 7!.

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A131678 a(n) = (Product_{i=1..8} n^i+i) / 8!.

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cp's OEIS Frontend

A131192 Numbers n >= 0 such that d(n) = (n^1 + 1)*(n^2 + 2)*...*(n^26 + 26) / 26! is nonintegral.

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Author

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Crossrefs

Programs

Maple

Extensions

A131677 a(n) = (Product_{i=1..7} n^i+i) / 7!.

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Author

Keywords

Comments

Links

Programs

Mathematica

PARI

Extensions

A131678 a(n) = (Product_{i=1..8} n^i+i) / 8!.

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Author

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Mathematica

PARI

Extensions

A131192 Numbers n >= 0 such that d(n) = (n^1 + 1)(n^2 + 2)...*(n^26 + 26) / 26! is nonintegral.