login
A316096
Numbers m such that A(m+1) = A(m) + 4, where A() = A005101() are the abundant numbers.
2
3, 6, 11, 13, 17, 18, 21, 24, 25, 32, 35, 40, 43, 46, 47, 50, 53, 60, 63, 64, 69, 72, 75, 78, 85, 88, 91, 94, 95, 100, 105, 106, 109, 112, 115, 117, 121, 124, 127, 130, 132, 136, 139, 140, 147, 148, 151, 154, 157, 159, 165, 168, 171, 176, 177, 180, 181, 184
OFFSET
1,1
LINKS
FORMULA
Sequence is { m | A005101(m+1) = A005101(m) + 4 }.
Sequence is { m | A125115(m) = 4 }.
a(n) = A091194(A316098(n)). - Amiram Eldar, Mar 01 2025
MAPLE
with(numtheory): A:=select(n->sigma(n)>2*n, [$1..1000]): a:=select(j->A[j+1]=A[j]+4, [$1..nops(A)-1]);
MATHEMATICA
Position[Map[{#1, #2 - 4} & @@ # &, Partition[Select[Range[10^3], DivisorSigma[1, #] > 2 # &], 2, 1]], _?(SameQ @@ # &)][[All, 1]] (* Michael De Vlieger, Jun 29 2018 *)
PROG
(GAP) A:=Filtered([1..1000], n->Sigma(n)>2*n);; a:=Filtered([1..Length(A)-1], i->A[i+1]=A[i]+4);
(PARI) list(lim) = {my(k = 1, k2, m = 0); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 4, print1(m, ", ")); m++; k1 = k2)); } \\ Amiram Eldar, Mar 01 2025
CROSSREFS
A316098 is the main sequence for this entry.
Numbers m such that A(m+1) = A(m) + k, where A() = A005101() are the abundant numbers: A169822 (k=1), A303741 (k=2), A316095 (k=3), this sequence (k=4), A316097 (k=6).
Sequence in context: A073942 A310089 A310090 * A310091 A136981 A316317
KEYWORD
nonn,changed
AUTHOR
Muniru A Asiru, Jun 25 2018
STATUS
approved