A373083 a(1) = 1; for n > 1, a(n) = a(n-1) + n if n is prime, else a(n) = a(n-1) + largest divisor of n < n.

1, 3, 6, 8, 13, 16, 23, 27, 30, 35, 46, 52, 65, 72, 77, 85, 102, 111, 130, 140, 147, 158, 181, 193, 198, 211, 220, 234, 263, 278, 309, 325, 336, 353, 360, 378, 415, 434, 447, 467, 508, 529, 572, 594, 609, 632, 679, 703, 710, 735, 752, 778, 831, 858, 869, 897

Offset: 1

Author

James C. McMahon, Jun 17 2024

Keywords

• nonn
• easy

Comments

Differs from A219730 at a(12).

Examples

			From _Michael De Vlieger_, Jun 23 2024: (Start)
Let lpf = A020639(n).
a(2) = 3 since 2 is prime, therefore a(1) + 2 = 3.
a(3) = 6 since 3 is prime, therefore a(2) + 3 = 6.
a(4) = 8 since 4 is not prime, therefore a(3) + 4/lpf(4) = 6 + 2 = 8.
a(5) = 13 since 5 is prime, therefore a(4) + 5 = 13.
a(6) = 16 since 6 is not prime, hence a(5) + 6/lpf(6) = 13 + 3 = 16, etc. (End)
		

Links

• James C. McMahon, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A117818, A219730.

Programs

Mathematica

a[1]=1;a[n_]:=If[PrimeQ[n],a[n-1]+n,a[n-1]+Divisors[n][[-2]]];Table[a[n],{n,56}]

PARI

alist(N) = my(r, d); vector(N, n, r+=if(2<#d=divisors(n), d[#d-1], d[#d])); \\ Ruud H.G. van Tol, Jul 11 2024

Formula

a(n) = a(n-1) + A117818(n) for n > 1. - Michael De Vlieger, Jun 23 2024