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.

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

Offset: 0

Author

Amarnath Murthy, May 06 2001

Keywords

• nonn
• base
• look
• easy

Comments

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

Examples

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

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.

Crossrefs

Cf. A264600, A264668.

Programs

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

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

Extensions

More terms from Erich Friedman, Jun 03 2001

a(0)=0 prepended by Alois P. Heinz, Nov 20 2015