A396784 Least positive integer k such that A001414(k+1) - A001414(k) = n.

5, 2, 1, 21, 10, 25, 12, 90, 50, 16, 22, 18, 221, 184, 45, 93, 154, 212, 28, 236, 144, 30, 46, 85, 147, 550, 2892, 36, 58, 177, 40, 42, 128, 201, 140, 213, 52, 452, 264, 304, 82, 121, 117, 133, 825, 294, 1188, 955, 868, 60, 243, 66, 106, 510, 200, 668, 663, 70

Offset

0,1

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Example

a(0) = 5 -> A001414(6) - A001414(5) = 5 - 5 = 0;
a(1) = 2 -> A001414(3) - A001414(2) = 3 - 2 = 1;
a(2) = 1 -> A001414(2) - A001414(1) = 2 - 0 = 2; etc.

Maple

with(numtheory): P:=proc(q) local a, b, c, k, n, v; v:=array(1..101);
for k from 1 to 101 do v[k]:=0; od; b:=[[0, 1]]; for n from 2 to q do a:=b; b:=ifactors(n+1)[2];
c:=add(b[k][1]*b[k][2], k=1..nops(b))-add(a[k][1]*a[k][2], k=1..nops(a)); if c>=0 and c<=100
then if v[c+1]=0 then v[c+1]:=n; fi; fi; od; op(v); end: P(3333);

Mathematica

A001414[n_] := A001414[n] = If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];
A396784[n_] := Module[{k = 1}, While[A001414[k+1] - A001414[k] != n, k++]; k];
Array[A396784, 100, 0] (* Paolo Xausa, Jun 08 2026 *)

Prog

(PARI) A001414(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
a(n) = my(k=1); while (A001414(k+1) - A001414(k) != n, k++); k; \\ Michel Marcus, Jun 08 2026

Crossrefs

Cf. A001414, A006145, A039752, A228126.

Sequence in context: A193590 A300051 A281890 * A342381 A341723 A111544

Adjacent sequences: A396779 A396780 A396781 * A396785 A396786 A396787

Keyword

nonn,easy

Author

Paolo P. Lava, Jun 05 2026

Status

approved