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A061486
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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.
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7
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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
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0,3
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COMMENTS
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LINKS
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EXAMPLE
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a(34) = 3 + 4 + 3*4 = 19, a(124) = (1+2+4)+(1*2+2*4+1*4)+(1*2*4) = 29.
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MAPLE
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with(combinat):
a:= n-> (l-> add(mul(l[i], i=w), w=choose(
nops(l)))-1)(convert(n, base, 10)):
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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