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A173106 Partial sums of A005100. 1
1, 3, 6, 10, 15, 22, 30, 39, 49, 60, 73, 87, 102, 118, 135, 154, 175, 197, 220, 245, 271, 298, 327, 358, 390, 423, 457, 492, 529, 567, 606, 647, 690, 734, 779, 825, 872, 921, 971, 1022, 1074, 1127, 1182, 1239, 1297, 1356, 1417, 1479, 1542, 1606, 1671, 1738, 1806, 1875, 1946 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of deficient numbers. The first 15 values are the same as the first 15 values of A025723 Index of 7^n within sequence of numbers of form 5^i*7^j. The subsequence of primes in the partial sum of deficient numbers begins: 3, 73, 197, 271, 457, 647, 971, 1297, 2731. The squares begin 1, 49, 529.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(n) = SUM[i=1..n]A005100(i) = SUM[i=1..n] {k such that sigma(k) < 2k}.

EXAMPLE

a(66) = 1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 10 + 11 + 13 + 14 + 15 + 16 + 17 + 19 + 21 + 22 + 23 + 25 + 26 + 27 + 29 + 31 + 32 + 33 + 34 + 35 + 37 + 38 + 39 + 41 + 43 + 44 + 45 + 46 + 47 + 49 + 50 + 51 + 52 + 53 + 55 + 57 + 58 + 59 + 61 + 62 + 63 + 64 + 65 + 67 + 68 + 69 + 71 + 73 + 74 + 75 + 76 +77 + 79 + 81 + 82 + 83 + 85 + 86.

MATHEMATICA

Accumulate[Select[Range[100], DivisorSigma[1, #]<2#&]]  (* Harvey P. Dale, Apr 11 2011 *)

CROSSREFS

Cf. A000040, A005100, A025723.

Sequence in context: A061304 A109442 A025723 * A022784 A025736 A022952

Adjacent sequences:  A173103 A173104 A173105 * A173107 A173108 A173109

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 09 2010

EXTENSIONS

Corrected and extended by Harvey P. Dale, Apr 11 2011.

STATUS

approved

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Last modified December 22 04:15 EST 2014. Contains 252326 sequences.