A091109 - OEIS

A091109

Number of occurrences of smallest prime factor in all partitions of n-th composite number: a(n)=A066633(A002808(n), A056608(n)).

3, 8, 19, 15, 41, 83, 160, 122, 295, 526, 911, 683, 1538, 2540, 853, 4115, 3050, 6551, 10269, 15873, 11664, 24222, 8415, 36532, 54509, 39784, 80524, 117862, 171036, 124143, 246211, 351769, 72718, 499042, 360550, 703268, 984857, 353996

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

n=2: A002808(2)=6=2*3 has A000041(6)=11 partitions: 6 = 5+1 = 4+2 = 4+1+1 = 3+3 = 3+2+1 = 3+1+1+1 = 2+2+2 = 2+2+1+1 = 2+1+1+1+1 = 1+1+1+1+1+1, 2 occurs 8 times, therefore a(2)=8.

MATHEMATICA

Count[Flatten[IntegerPartitions[#]], FactorInteger[#][[1, 1]]]&/@ Select[ Range[ 60], CompositeQ] (* Harvey P. Dale, Sep 08 2018 *)

CROSSREFS

Cf. A002808, A000041, A056608, A020639, A091114.

Sequence in context: A023371 A358984 A124086 * A219391 A123982 A171308

Adjacent sequences: A091106 A091107 A091108 * A091110 A091111 A091112

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 22 2004

STATUS

approved