The On-Line Encyclopedia of Integer Sequences (OEIS)

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A280242

Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^2, where omega(k) is the number of distinct prime factors (A001221).
(history; published version)

#7 by N. J. A. Sloane at Sun Apr 23 23:59:15 EDT 2017

STATUS

proposed

approved

#6 by G. C. Greubel at Sun Apr 23 21:05:04 EDT 2017

STATUS

editing

proposed

#5 by G. C. Greubel at Sun Apr 23 21:04:50 EDT 2017

LINKS

G. C. Greubel, <a href="/A280242/b280242.txt">Table of n, a(n) for n = 0..1000</a>

STATUS

approved

editing

#4 by N. J. A. Sloane at Sat Dec 31 01:29:49 EST 2016

STATUS

proposed

approved

#3 by Ilya Gutkovskiy at Thu Dec 29 16:49:25 EST 2016

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Thu Dec 29 16:16:51 EST 2016

NAME

allocated for Ilya GutkovskiyExpansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^2, where omega(k) is the number of distinct prime factors (A001221).

DATA

0, 0, 0, 0, 1, 2, 3, 4, 3, 4, 5, 6, 6, 6, 5, 6, 7, 4, 7, 6, 8, 8, 7, 4, 8, 6, 7, 8, 8, 6, 10, 6, 11, 8, 13, 8, 14, 4, 9, 8, 12, 6, 10, 6, 10, 10, 11, 4, 14, 6, 13, 8, 12, 4, 15, 6, 14, 8, 11, 4, 14, 6, 11, 8, 13, 4, 18, 4, 14, 10, 14, 4, 18, 6, 13, 12, 14, 6, 18, 4, 16, 8, 11, 8, 20, 6, 17, 8, 14, 6, 22, 8, 16, 6, 13, 4, 20, 4

OFFSET

0,6

COMMENTS

Number of ordered ways of writing n as the sum of two prime powers (1 excluded).

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>

FORMULA

G.f.: (Sum_{k>=2} floor(1/omega(k))*x^k)^2.

EXAMPLE

a(6) = 3 because we have [4, 2], [3, 3] and [2, 4].

MATHEMATICA

nmax = 97; CoefficientList[Series[(Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^2, {x, 0, nmax}], x]

CROSSREFS

Cf. A001221, A071330, A071331, A073610, A095840, A246655.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Dec 29 2016

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Thu Dec 29 16:16:51 EST 2016

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved