A252737 Row sums of irregular tables A005940, A163511, and A332977.

1, 2, 7, 28, 130, 702, 4384, 31516, 260068, 2445372, 25796360, 299286550, 3751803964, 50211590696, 712746859372, 10697637496288, 169490803535680, 2830925427778810, 49785906936838240, 921273098388684878, 17944637546960083042, 368472898102440537484, 7993616254370783660414, 183539682466936703629744

Offset: 0

Author

Antti Karttunen, Dec 21 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Row sums of tables A005940, A163511, and A332977.

Cf. A252738 (row products).

Cf. A000079, A000225, A252745, A252746.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, add(b(n-`if`(
      i=0, j, 1), j)*ithprime(j), j=1..`if`(i=0, n, i)))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..23);  # Alois P. Heinz, Mar 04 2020

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n - If[i == 0, j, 1], j]* Prime[j], {j, 1, If[i == 0, n, i]}]];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jan 03 2022, after Alois P. Heinz *)

PARI

allocatemem(234567890);
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A252737print(up_to_n) = { my(s, i=0, n=0); for(n=0, up_to_n, if(0 == n, s = 1, if(1 == n, s = 2; lev = vector(1); lev[1] = 2, oldlev = lev; lev = vector(2*length(oldlev)); s = 0; for(i = 0, (2^(n-1))-1, lev[i+1] = if((i%2),A003961(oldlev[(i\2)+1]),2*oldlev[(i\2)+1]); s += lev[i+1]))); write("b252737.txt", n, " ", s)); };
A252737print(23); \\ Terms a(0) .. a(23) were computed with this program.

Scheme

(define (A252737 n) (if (zero? n) 1 (add A163511 (A000079 (- n 1)) (A000225 n))))

Scheme

(define (A252737 n) (if (zero? n) 1 (add (COMPOSE A005940 1+) (A000079 (- n 1)) (A000225 n))))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))
(define (COMPOSE . funlist) (cond ((null? funlist) (lambda (x) x)) (else (lambda (x) ((car funlist) ((apply COMPOSE (cdr funlist)) x))))))

Formula

a(0) = 1; for n>1: a(n) = Sum_{k = A000079(n-1) .. A000225(n)} A163511(k) = Sum_{k = 2^(n-1) .. (2^n)-1} A163511(k).