

A061486


Let the number of digits in n be k; a(n) = sum of the products of the digits of n taken r at a time where r ranges from 1 to k.


7



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 8, 17, 26, 35, 44, 53, 62, 71, 80, 89, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 1, 3
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OFFSET

0,3


COMMENTS

Differs from A264600 first at n=101: a(101) = 3 != A264600(101) = 12.  Alois P. Heinz, Nov 20 2015


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..20000
Eric Weisstein's World of Mathematics, Symmetric polynomial.
Wikipedia, Elementary symmetric polynomial.


EXAMPLE

a(34) = 3 + 4 + 3*4 = 19, a(124) = (1+2+4)+(1*2+2*4+1*4)+(1*2*4) = 29.


MAPLE

with(combinat):
a:= n> (l> add(mul(l[i], i=w), w=choose(
nops(l)))1)(convert(n, base, 10)):
seq(a(n), n=0..101); # Alois P. Heinz, Nov 20 2015


PROG

(PARI) sympol(X, n)=my(s=0); forvec(i=vector(n, j, [1, #X]), s+=prod(k=1, n, X[i[k]]), 2); s ;
a(n) = my(d=digits(n)); sum(k=1, #d, sympol(d, k)); \\ Michel Marcus, Apr 06 2021


CROSSREFS

Cf. A264600, A264668.
Sequence in context: A135208 A259043 A156207 * A264600 A138470 A325454
Adjacent sequences: A061483 A061484 A061485 * A061487 A061488 A061489


KEYWORD

nonn,base,look,easy


AUTHOR

Amarnath Murthy, May 06 2001


EXTENSIONS

More terms from Erich Friedman, Jun 03 2001
a(0)=0 prepended by Alois P. Heinz, Nov 20 2015


STATUS

approved



