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A062761 Number of powerful numbers between 2^(n-1)+1 and 2^n. 2
1, 0, 1, 1, 2, 3, 3, 7, 8, 12, 17, 25, 36, 50, 74, 105, 152, 213, 306, 437, 620, 882, 1256, 1781, 2531, 3588, 5091, 7221, 10225, 14504, 20542, 29101, 41214, 58369, 82638, 116986, 165610, 234387, 331738, 469429, 664291, 939924, 1329876, 1881500, 2661826, 3765629 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Daniel Suteu, Table of n, a(n) for n = 0..90

FORMULA

Number of terms x from A001694 for which A029837(x)=n.

Sum_{k=0..n} a(k) = A062762(n). - Daniel Suteu, Feb 18 2020

EXAMPLE

64 < {72,81,100,108,121,125,128} <= 128, i.e., 7 powerful numbers are between 2^6 and 2^7, so a(7)=7.

PROG

(PARI) a(n) = my(ka = if (n==0, 1, 2^(n-1)+1)); #select(x->ispowerful(x), [ka..2^n]); \\ Michel Marcus, Aug 25 2019

(PARI) Q(n) = my(s=0); forsquarefree(k=1, sqrtnint(n, 3), s += sqrtint(n\k[1]^3)); s;

a(n) = if(n==0, 1, Q(2^n) - Q(2^(n-1))); \\ Daniel Suteu, Feb 18 2020

CROSSREFS

Cf. A001694, A029837, A036380, A036386, A062762.

Sequence in context: A209169 A222294 A181850 * A117524 A308513 A045683

Adjacent sequences:  A062758 A062759 A062760 * A062762 A062763 A062764

KEYWORD

nonn,changed

AUTHOR

Labos Elemer, Jul 16 2001

EXTENSIONS

a(19)-a(29) from Daniel Suteu, Aug 25 2019

a(30)-a(45) from Daniel Suteu, Feb 18 2020

STATUS

approved

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Last modified February 27 22:50 EST 2020. Contains 332319 sequences. (Running on oeis4.)