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A110765 Let n in binary be a k-digit number say abbaaa... where a = 1 and b = 0. a(n) = 2^a*3^b*5^b*7*a... primes in increasing order raised to the powers starting from the MSB. 4
2, 2, 6, 2, 10, 6, 30, 2, 14, 10, 70, 6, 42, 30, 210, 2, 22, 14, 154, 10, 110, 70, 770, 6, 66, 42, 462, 30, 330, 210, 2310, 2, 26, 22, 286, 14, 182, 154, 2002, 10, 130, 110, 1430, 70, 910, 770, 10010, 6, 78, 66, 858, 42, 546, 462, 6006, 30, 390, 330, 4290, 210, 2730 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms have 2-adic valuation equal to 1, i.e., they equal twice an odd (and squarefree) number, since the first digit in base two will always be "1". - M. F. Hasler, Mar 25 2011

2 appears at index n = 2^k for k >= 0, since such n_2 begins with "1" followed by k zeros, and 2^1 * 3^0 * ... * p_(k+1)^0 = 2. - Michael De Vlieger, Feb 28 2021

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

a(7) = 2*3*5 = 30. binary 7 = 111,

a(10) = 2^1*3^0*5^1*7^0 =10, binary(10) = 1010.

MATHEMATICA

Array[Times @@ Prime@ Flatten@ Position[#, 1] &@ IntegerDigits[#, 2] &, 61] (* Michael De Vlieger, Feb 28 2021 *)

PROG

(PARI) a(n)=factorback(Mat(vector(#n=binary(n), j, [prime(j), n[j]])~))

(PARI) a(n)=prod(j=1, #n=binary(n), prime(j)^n[j])  \\ M. F. Hasler, Mar 25 2011

(Haskell)

a110765 = product . zipWith (^) a000040_list .  reverse . a030308_row

-- Reinhard Zumkeller, Aug 28 2014

(Python)

from sympy import prime

from operator import mul

from functools import reduce

def A110765(n):

....return reduce(mul, (prime(i) for i, d in enumerate(bin(n)[2:], start=1) if int(d)))

# implementation using recursion

def _A110765(n):

....nlen = len(n)

....return _A110765(n[:-1])*(prime(nlen) if int(n[-1]) else 1) if nlen > 1 else int(n) + 1

def A110765(n):

....return _A110765(bin(n)[2:])

# Chai Wah Wu, Sep 05 2014

CROSSREFS

Cf. A110766.

Cf. A030308, A000040, A019565.

Sequence in context: A232625 A099985 A298299 * A176991 A264666 A283362

Adjacent sequences:  A110762 A110763 A110764 * A110766 A110767 A110768

KEYWORD

base,easy,nonn,look

AUTHOR

Amarnath Murthy, Aug 12 2005

EXTENSIONS

More terms from Stacy Hawthorne (shawtho1(AT)ashland.edu), Oct 31 2005

STATUS

approved

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Last modified May 14 16:46 EDT 2021. Contains 343890 sequences. (Running on oeis4.)