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.

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

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