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A275474 Numbers n for which e_n(2*i)=e_n(2*i+1), for all i>=1, where e_n(k)>=0 denote the exponent of prime(k) in the prime power representation of n. 1
1, 2, 4, 8, 15, 16, 30, 32, 60, 64, 77, 120, 128, 154, 221, 225, 240, 256, 308, 437, 442, 450, 480, 512, 616, 874, 884, 899, 900, 960, 1024, 1155, 1232, 1517, 1748, 1768, 1798, 1800, 1920, 2021, 2048, 2310, 2464, 3034, 3127, 3315, 3375, 3496, 3536, 3596, 3600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

There exists a permutation alpha of the sequence such that {alpha(a(n))} is a completely multiplicative function.

Numbers which are the product of zero or more of {2, 3*5, 7*11, 13*17, 19*23, ...} with multiplicity. - Charles R Greathouse IV, Jul 30 2016

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

1 is a member, since all e_1(k)=0;

Powers 2^m, m>=1, are members, since e_2^m(k)=0, for all k>=2;

15 is a member, since e_15(2)*e_15(3)=1;

n = 2983500 is a member, since e_n(1)=2, e_n(2)=e_n(3)=3 and e_n(6)=e_n(7)=1, all other e_n(k)=0.

PROG

(PARI) is(n)=my(f=factor(n>>valuation(n, 2))); if (#f~%2, return(0)); for(i=1, #f~/2, if(f[2*i-1, 2]!=f[2*i, 2] || nextprime(f[2*i-1, 1]+1)!=f[2*i, 1], return(0))); for(i=1, #f~/2, if(primepi(f[2*i, 1])%2==0, return(0))); 1 \\ Charles R Greathouse IV, Jul 30 2016

(PARI) list(lim)=my(v=List([1, 2]), p=3, pStart=2, pEnd, start=2, end, nStart, t); lim\=1; forprime(q=5, sqrtint(lim+1)+1, p=if(p, listput(v, p*q); 0, q)); end=pEnd=#v; for(n=2, logint(lim, 2), nStart=end+1; for(i=start, end, for(j=pStart, pEnd, t=v[i]*v[j]; if(t>lim, break); listput(v, t))); start=nStart; end=#v); Set(v) \\ Charles R Greathouse IV, Jul 30 2016

CROSSREFS

Cf. A000040, A001248, A089581, A275246, A275248, A275249, A275251, A275252, A275253, A275407.

Sequence in context: A277166 A078613 A072202 * A076351 A140117 A039743

Adjacent sequences:  A275471 A275472 A275473 * A275475 A275476 A275477

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Jul 29 2016

EXTENSIONS

More terms from Peter J. C. Moses, Jul 29 2016

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)