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 1-2 of 2 results.

A131190 Numbers n>=0 such that d(n) = (n^1 + 1) (n^2 + 2) ... (n^25 + 25) / 25! is nonintegral.

Original entry on oeis.org

2, 7, 12, 18, 22, 27, 29, 37, 40, 47, 51, 52, 62, 72, 73, 77, 84, 87, 95, 97, 102, 106, 112, 122, 127, 128, 137, 139, 147, 150, 152, 161, 162, 172, 177, 183, 187, 194, 197, 202, 205, 212, 216, 222, 227, 237, 247, 249, 252, 260, 262, 271, 272, 277, 282, 287, 293, 297, 302, 304, 312, 315, 322, 326, 327, 337
Offset: 1

Views

Author

Alexander R. Povolotsky, Sep 25 2007

Keywords

Comments

If n is in this sequence the so is n+6050. - Max Alekseyev, Feb 02 2015

Crossrefs

Cf. A129995, A131189, A131191, A131192, A131685

Programs

  • PARI
    { is_A131190(n) = setsearch([2,12,22,27,37,47],n%50) || ( (n%11)==7 && (n%121)!=117 ) } /* Max Alekseyev, Feb 02 2015 */

Formula

Notice that 25! = 2^22 * 3^10 * 5^6 * 7^3 * 11^2 * 13 * 17 * 19 * 23. The value of (n^1+1)(n^2+2)...(n^25+25) is always divisible by all these prime powers, except 5^6 and 11^2. There is no divisibility by 5^6 for n in {50m+2, 50m+12, 50m+22, 50m+27, 50m+37, 50m+47} and by 11^2 for n in {11m+7} \ {121m+117}. Therefore, the sequence is the union {50m+2} U {50m+12} U {50m+22} U {50m+27} U {50m+37} U {50m+47} U ( {11m+7} \ {121m+117} ). - Max Alekseyev, Nov 10 2007

Extensions

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

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

Original entry on oeis.org

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

Views

Author

Alexander R. Povolotsky, Sep 25 2007

Keywords

Comments

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

Crossrefs

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

Programs

  • Maple
    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

Extensions

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
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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