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.

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A048622 Difference of maximal and central values of A001222 when applied to {C(n,k)} set.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 3, 2, 1, 1, 3, 2, 1, 0, 2, 1, 2, 1, 1, 0, 0, 0, 2, 2, 1, 0, 1, 1, 3, 2, 3, 2, 0, 0, 2, 0, 0, 0, 4, 3, 4, 3, 2, 2, 3, 3, 5, 4, 3, 2, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 0, 0, 1, 1, 3, 2, 1, 0, 0, 0, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2
Offset: 1

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Examples

			n=24: the sums of prime factor exponents when k runs from 0 to 24 are {0,4,4,5,5,7,6,8,6,8,8,9,7,9,8,8,6,8,6,7,5,5,4,4,0}. The central value is 7, the maximal is 9 so a(24)=9-7.
		

Crossrefs

Programs

  • PARI
    a(n) = vecmax(apply(bigomega, vector(n+1, k, binomial(n,k-1)))) - bigomega(binomial(n, n\2)); \\ Michel Marcus, Jun 25 2021

Formula

a(n) = Max_k {A001222(C(n, k))} - A001222(A001405(n)).
a(n) = A048620(n) - A048621(n). - Sean A. Irvine, Jun 24 2021

A048682 a(n) is the difference between maximal and central squarefree kernel numbers dividing values of {binomial(n,k)} or A001405(n), respectively.

Original entry on oeis.org

0, 0, 0, 0, 0, 5, 0, 0, 0, 168, 0, 0, 0, 2145, 2860, 0, 0, 0, 0, 33592, 117572, 470288, 0, 0, 297160, 4791705, 2674440, 12900240, 28134060, 10835415, 0, 0, 0, 2074316640, 0, 0, 2524661700, 31810737420, 39384722520, 0, 0, 0, 82334307276, 1235014609140
Offset: 1

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Examples

			n=10: the squarefree kernels are {1, 10, 15, 30, 210, 42, 210, 30, 15, 10, 1}. The maximal value is 210 and the central one is 42. Thus a(10) = 210 - 42 = 168.
		

Crossrefs

Analogous cases for A001222, A000005 as applied to {binomial(n, k)} are given in A048623, A020740.
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