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 A063519 Least composite k such that phi(k+12n) = phi(k)+12n and sigma(k+12n) = sigma(k) + 12n where phi is the Euler totient function and sigma is the sum of divisors function. 0
 65, 95, 341, 95, 161, 115, 629, 203, 145, 203, 365, 155, 185, 155, 301, 185, 329, 235, 1541, 287, 185, 287, 413, 205, 329, 215, 469, 215, 905, 371, 365, 305, 553, 371, 1037, 235, 1145, 623, 445, 371, 35249, 295, 1133, 371, 497, 515, 749, 413, 305, 671, 565 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No such simultaneous solutions were found if d=12n+6. LINKS Table of n, a(n) for n=1..51. FORMULA a(n) = Min{k: phi(k+12n) = phi(k)+12n and sigma(k+12n) = sigma(k)+12n and k is composite} with phi(k) = A000010(k) and sigma(k) = A000203(k). EXAMPLE a(97)=10217 because 10217 is composite, phi(10217)+1164 = 9600+1164 = 10764 = phi(11381) and sigma(10217)+1164 = 10836+1164 = 12000 = sigma(11381) with 1164 = 12*97 and there is no smaller composite with these properties. CROSSREFS A000010, A000203, A054904, A054905, A055458. Sequence in context: A020194 A094447 A020224 * A299456 A300094 A350241 Adjacent sequences: A063516 A063517 A063518 * A063520 A063521 A063522 KEYWORD nonn AUTHOR Labos Elemer, Aug 01 2001 EXTENSIONS Name corrected by Sean A. Irvine, Apr 30 2023 STATUS approved

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Last modified June 4 07:15 EDT 2023. Contains 363118 sequences. (Running on oeis4.)