A275306 -id:A275306 - cp's OEIS frontend

A073718 Powers of 2 with composite exponents.

16, 64, 256, 512, 1024, 4096, 16384, 32768, 65536, 262144, 1048576, 2097152, 4194304, 16777216, 33554432, 67108864, 134217728, 268435456, 1073741824, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736

Offset: 1

Labos Elemer, Aug 05 2002

Index to divisibility sequences

Cf. A000079, A002808, A275306.

Table[2^FixedPoint[n+PrimePi[ # ]+1&, n], {n, 1, 30}]

for(n=4,100,if(!isprime(n),print1(2^n", "))) \\ Charles R Greathouse IV, Apr 09 2012

a(n) = 2^A002808(n) = A000079(A002808(n)).

Sum_{n>=1} 1/a(n) = A275306. - Amiram Eldar, Aug 11 2020

A119524 Decimal expansion of Sum_{k >= 1} ((-1)^A010051(k))/2^k.

Original entry on oeis.org

1, 7, 0, 6, 3, 4, 9, 8, 0, 2, 9, 7, 7, 7, 6, 6, 7, 9, 5, 0, 3, 7, 8, 0, 7, 5, 5, 6, 9, 1, 3, 8, 4, 5, 8, 3, 2, 6, 8, 4, 5, 1, 5, 2, 3, 7, 2, 4, 1, 6, 6, 0, 4, 4, 2, 6, 3, 5, 0, 9, 1, 7, 1, 0, 2, 2, 7, 1, 8, 0, 7, 8, 7, 6, 1, 2, 8, 5, 3, 3, 1, 6, 0, 7, 4, 1, 9, 9, 0, 3, 1, 4, 3, 0, 4, 8, 4, 4, 4, 1

Offset: 0

Roger L. Bagula, May 27 2006

			0.17063498029777667950378075569138458326845152372416604426350917102271807...

Cf. A010051, A065855, A119523, A275306.

suminf(k=1, (-1)^isprime(k)/2^k) \\ Michel Marcus, Jan 16 2024

Equals Sum_{k >= 1} (k - 1 - PrimePi(k))/2^k = Sum_{k >= 1} A065855(k)/2^k.
From Antonio Graciá Llorente, Jan 14 2024: (Start)
Equals Sum_{k >= 2} A005171(k)/2^(k-1).
Equals Sum_{k >= 1} ((-1)^A010051(k))/2^k.
Equals 2*A275306. (End)

Edited and corrected by N. J. A. Sloane, Nov 17 2006

Better name from Joerg Arndt, Jan 16 2024

cp's OEIS Frontend

A073718 Powers of 2 with composite exponents.

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