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A statue on the grounds of the Federal Reserve Bank in Washington. Photographer: Luke Sharrett/Bloomberg
Updated April 7, 2016 4:53 p.m. ET
Research firm Mediabrands has taken a new look at the emerging credit card business, focusing on payments. The research finds that retailers and other financial institutions have more than $1 trillion of potential annual spending with credit cards, and that the industry is moving away from cash-based transactions. The research firm also found that two of the nation’s four biggest credit card companies — Bank of America Corp., JPMorgan Chase & Co. — account for roughly half the market.
The findings are contained in a new report, released Wednesday, called “Findex: The Future of the Credit Card Business.”Q:
Sum of all natural logarithms of the prime factors of a number
Can someone explain me why this function sums all the natural logarithms of the prime factors of a number?
def logn_sum(x):
a, b = 1, x
while x % b == 0:
b = b ** 2
a = a + b
return a
A:
Take this prime:
4
when it’s factored, it has factors, 2, 2, 2, and 2.
exp(ln(2^2^2^2) = 4
When you take the natural log of each of these factors, you get ln(2^2) = 2, ln(2^2^2) = 4, ln(2^2^2^2) = 4, and ln(2^2^2^2^2) = 4.
Now, for any natural number, you can get the sum of all ln(2^k), where k is a factor.
ln(x) = sum([ln(p^k
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