A278294 - OEIS

A278294

a(n) = first term in A278291 with n prime factors.

3, 10, 28, 136, 945, 5265, 29889, 50625, 203392, 3290625, 6082048, 32536000, 326481921, 3274208001, 6929459200, 72523096065, 37694578689, 471672487936, 11557226700801, 54386217385984, 50624737509376, 275892612890625, 4870020829413376, 68091093855502336, 2280241934368768

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OFFSET

1,1

COMMENTS

a(n)-1 is the first term in A115186 with n prime factors, by definition.

If f(n) is the index of the first occurrence of n in A278293, a(n)=A278291(f(n)), by definition.

LINKS

Ely Golden, Table of n, a(n) for n = 1..25

EXAMPLE

a(2)=10, as it is the first term of A278291 with 2 prime factors.

a(3)=28, as it is the first term of A278291 with 3 prime factors.

MATHEMATICA

Function[w, Flatten@ Map[w[[#]] &, #] &@ Map[First, DeleteCases[#, w_ /; Length@ w == 0]] &@ Map[Position[w, k_ /; PrimeOmega@k == #] &, Range@ 9]]@ Select[Range[10^6], Equal @@ Map[PrimeOmega, {# - 1, #}] &] (* Michael De Vlieger, Dec 01 2016 *)

PROG

(Java) import java.math.BigInteger;

public class A278294{

public static void main(String[] args)throws Exception{

BigInteger dim0=numberOfPrimeFactors(BigInteger.valueOf(2)); //note that this method must be manually implemented by the user

BigInteger dim1;

BigInteger maxdim=BigInteger.ONE;

BigInteger counter=BigInteger.valueOf(3);

long index=1;

while(index<=20){

dim1=numberOfPrimeFactors(counter);

if(dim1.equals(dim0)&&maxdim.testBit(dim1.intValue())==false){System.out.println(dim1+" "+counter); maxdim=maxdim.setBit(dim1.intValue()); index++; }

dim0=dim1;

counter=counter.add(BigInteger.ONE);

}

(SageMath)

def bigomega(x):

s=0;

f=list(factor(x));

for c in range(len(f)):

s+=f[c][1]

return s;

dim0=bigomega(2);

maxdim=1

counter=3

index=1

while(index<=20):

dim1=bigomega(counter);

if((dim1==dim0)&((maxdim&(1<<dim1))==0)):

print(str(index)+" "+str(counter))

maxdim=maxdim|(1<<dim1);

index+=1;

dim0=dim1;

counter+=1;

CROSSREFS

Cf. A115186.

Sequence in context: A239885 A262251 A246974 * A260811 A108912 A350821

Adjacent sequences: A278291 A278292 A278293 * A278295 A278296 A278297

KEYWORD

nonn

AUTHOR

Ely Golden, Nov 16 2016

STATUS

approved