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 1-3 of 3 results.

A272080 Row sums of A238498.

Original entry on oeis.org

1, 2, 5, 10, 22, 38, 110, 178, 378, 698, 1766, 2618, 7442, 11006, 26482, 58226, 123698, 178310, 502490, 719802, 1814954, 3737154, 8601674, 11944562, 33535586, 54001022, 120654206, 217935362, 518197346, 718356542, 2441734706, 3392584002, 7055236194, 13981570658
Offset: 0

Views

Author

Tom Edgar, Apr 19 2016

Keywords

Links

Crossrefs

Cf. A001615, A238498.

Programs

  • Sage
    P=[0]+[i*prod([(1+1/x) for x in prime_divisors(i)]) for i in [1..100]]
Tr=[[prod(P[1:n+1])/(prod(P[1:k+1])*prod(P[1:(n-k)+1])) for k in [0..n]] for n in [0..len(P)-1]]
print([sum(x) for x in Tr])

A272178 Absolute value of alternating row sum of row 2n in A238498.

Original entry on oeis.org

1, 1, 2, 10, 54, 322, 1294, 4526, 20782, 93814, 371110, 1780294, 6733918, 22513642, 92018398, 461754862, 1297077342, 5790726826, 32850248974, 94597335398, 454725608974, 2080853077822, 6173935052878, 29922219241486, 116844904688830, 448338212337298, 1975870364475334
Offset: 0

Views

Author

Tom Edgar, Apr 21 2016

Keywords

Comments

The alternating row sums of the odd-indexed rows are 0.

Links

Crossrefs

Cf. A001615, A238498, A272080.

Programs

  • Sage
    P=[0]+[i*prod([(1+1/x) for x in prime_divisors(i)]) for i in [1..100]]
Tr=[[prod(P[1:n+1])/(prod(P[1:k+1])*prod(P[1:(n-k)+1])) for k in [0..n]] for n in [0..len(P)-1]]
L=[sum((-1)^(i)*x[i] for i in [0..len(x)-1]) for x in Tr]
[abs(y) for y in L if y!=0]

Formula

For n>0, a(n) = Sum_{k=0..2n}(-1)^(k+1)*A238498(2n,k).

A175836 a(n) = Product_{i=1..n} psi(i) where psi is the Dedekind psi function (A001615).

Original entry on oeis.org

1, 3, 12, 72, 432, 5184, 41472, 497664, 5971968, 107495424, 1289945088, 30958682112, 433421549568, 10402117189632, 249650812551168, 5991619501228032, 107849151022104576, 3882569436795764736
Offset: 1

Views

Author

Enrique Pérez Herrero, Sep 18 2010

Keywords

Comments

a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = A060648(gcd(i,j)) for 1 <= i,j <= n, note that A060648 is the Inverse Möbius transform of A001615. - Enrique Pérez Herrero, Aug 12 2011

Links

Crossrefs

Cf. A001615, A001088, A059381, A059382, A059383, A059384, A238498.
Cf. A239672.

Programs

  • Haskell
    a175836 n = a175836_list !! (n-1)
a175836_list = scanl1 (*) a001615_list
-- Reinhard Zumkeller, Mar 01 2014
  • Maple
    A175836 := proc(n) option remember; local p; `if`(n<2,1, n*mul(1+1/p,p=factorset(n))*A175836(n-1)) end: # Peter Luschny, Feb 28 2014
  • Mathematica
    JordanTotient[n_,k_:1]:=DivisorSum[n,#^k*MoebiusMu[n/# ]&]/;(n>0)&&IntegerQ[n];
DedekindPsi[n_]:=JordanTotient[n,2]/EulerPhi[n];
A175836[n_]:=Times@@DedekindPsi/@Range[n]
  • PARI
    a=direuler(p=2, 100, (1+X)/(1-p*X));for(i=2,#a,a[i]*=a[i-1]);a
\\ Charles R Greathouse IV, Jul 29 2011

Formula

a(n) = A059381(n)/A001088(n).
Showing 1-3 of 3 results.

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

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