A189803 Composite numbers n such that n'' = n'-1 where n' and n'' are the first and the second arithmetic derivative of n.

9, 185, 341, 377, 437, 9005, 30413, 33953, 41009, 51533, 82673, 92909, 103073, 126509, 143009, 165773, 181793, 184973, 191309, 228653, 231713, 246893, 291233, 311309, 316973, 319793, 329357, 353009, 358433, 374513, 398093, 405809, 431009, 460193, 467309

Offset

1,1

Comments

The sequence A189710 (n"=n'-1) includes all prime numbers because p'=1 and p" = 0. Composite numbers are not very frequent.

Are all terms semiprimes? These terms appear to be p*q such that p+q is a term in A054377, which has solutions to the equation n' = n-1. - T. D. Noe, Apr 27 2011

Links

Table of n, a(n) for n=1..35.

Example

9' = 6, 9''= 6'= 5, 9" = 9'- 1 -> 9 is in the sequence.

Prog

(PARI) ader(n) = my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1])); \\ A003415
isok(k) = if (!isprime(k), my(d=ader(k)); ader(d) == d - 1); \\ Michel Marcus, Mar 13 2023

Crossrefs

Cf. A002808, A003415, A054377, A068346, A189710.

Sequence in context: A064332 A319798 A300598 * A216409 A171194 A196297

Adjacent sequences: A189800 A189801 A189802 * A189804 A189805 A189806

Keyword

nonn

Author

Giorgio Balzarotti, Apr 27 2011

Status

approved