Prime Factors

The number of Distinct Prime Factors of a number is denoted . The first few values for ,2, ... are 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, ... (Sloane's A001221; top figure). Thenumber of not necessarily distinct prime factors of a number is denoted . The first few values for ,2, ... are 0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, ... (Sloane's A001222; bottom figure).

References

Sloane, N. J. A. SequencesA001222/M0094and A001221/M0056in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

• Cauchy Boundary Conditions
• Cauchy Criterion
• Cauchy Distribution
• Cauchy Equation
• Cauchy Functional Equation
• Cauchy-Hadamard Theorem
• Cauchy Inequality
• Cauchy Integral Formula
• Cauchy Integral Test
• Cauchy Integral Theorem
• Cauchy-Kovalevskaya Theorem
• Cauchy-Lagrange Identity
• Cauchy-Maclaurin Theorem
• Cauchy Mean Theorem
• Cauchy Principal Value
• Cauchy Problem
• Cauchy Ratio Test
• Cauchy Remainder Form
• Cauchy-Riemann Equations
• Cauchy Root Test
• Cauchy-Schwarz Integral Inequality
• Cauchy-Schwarz Sum Inequality
• Cauchy's Cosine Integral Formula
• Cauchy Sequence
• Cauchy's Formula