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

0,2

Links

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

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).

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 *)

Prog

(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, two alternative versions)
(define (A252737 n) (if (zero? n) 1 (add A163511 (A000079 (- n 1)) (A000225 n))))
(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))))))

Crossrefs

Row sums of tables A005940, A163511, and A332977.

Cf. A252738 (row products).

Cf. A000079, A000225, A252745, A252746.

Sequence in context: A118926 A127084 A362555 * A217203 A052319 A127783

Adjacent sequences: A252734 A252735 A252736 * A252738 A252739 A252740

Keyword

nonn

Author

Antti Karttunen, Dec 21 2014

Status

approved