A061141 Compute sum of divisors of the prime(n+1)-prime(n)-1 composite numbers between two consecutive primes; choose the largest.

7, 12, 18, 28, 31, 39, 42, 60, 72, 91, 90, 96, 84, 124, 120, 168, 144, 144, 195, 168, 186, 224, 252, 217, 216, 210, 280, 248, 360, 255, 336, 288, 403, 372, 392, 378, 294, 480, 372, 546, 384, 508, 399, 468, 576, 600, 504, 560, 450, 546, 744, 504, 728, 588, 720

Offset

2,1

Links

Michael S. Branicky, Table of n, a(n) for n = 2..10001 (terms 2..1002 from Harry J. Smith)

Formula

a(n) = Max{sigma(c); p(n+1) > c > p(n)}, c is composite, p(n) is the n-th prime and sigma=A000203().

Mathematica

Max[DivisorSigma[1, Range[#[[1]]+1, #[[2]]-1]]]&/@Partition[Prime[ Range[2, 60]], 2, 1] (* Harvey P. Dale, May 19 2017 *)

Prog

(PARI) { n=1; q=3; forprime (p=5, prime(1003), a=0; for (i=q + 1, p - 1, a=max(sigma(i), a)); q=p; write("b061141.txt", n++, " ", a) ) } \\ Harry J. Smith, Jul 18 2009
(Python)
from sympy import prime, divisor_sigma as sigma
def a(n): return max(sigma(c) for c in range(prime(n)+1, prime(n+1)))
print([a(n) for n in range(2, 57)]) # Michael S. Branicky, Jul 12 2021

Crossrefs

Cf. A000040, A000203, A061120, A335579.

Sequence in context: A022953 A030714 A190036 * A256381 A272975 A190495

Adjacent sequences: A061138 A061139 A061140 * A061142 A061143 A061144

Keyword

nonn

Author

Labos Elemer, May 29 2001

Extensions

Offset changed by Michael S. Branicky, Jul 12 2021

Status

approved