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A067692 a(n) = sum{d*t : 0<d<=t<=n and d|n and t|n}. 12
1, 7, 13, 35, 31, 97, 57, 155, 130, 227, 133, 497, 183, 413, 418, 651, 307, 988, 381, 1155, 762, 953, 553, 2225, 806, 1307, 1210, 2093, 871, 3242, 993, 2667, 1762, 2183, 1802, 5096, 1407, 2705, 2418, 5155, 1723, 5858 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For p prime: a(p) = 1+p+p^2, a(A000040(k))=A060800(k).

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 1/2*(sigma_1(n)^2+sigma_2(n)), cf. A000203, A001157.

EXAMPLE

a(6) = 1*1+1*2+1*3+1*6+2*2+2*3+2*6+3*3+3*6+6*6 = 1+2+3+6+4+6+12+9+18+36 = 97.

MATHEMATICA

Table[(DivisorSigma[1, n]^2+DivisorSigma[2, n])/2, {n, 50}] (* Harvey P. Dale, Jan 31 2015 *)

PROG

(PARI) a(n)=my(D=sigma(n)); sumdiv(n, t, D-=t; t*(D+t)) \\ Charles R Greathouse IV, Aug 21 2011

(PARI) a(n)=(sigma(n)^2+sigma(n, 2))/2 \\ Charles R Greathouse IV, Aug 21 2011

CROSSREFS

Sequence in context: A061204 A060983 A001001 * A117706 A066673 A267985

Adjacent sequences:  A067689 A067690 A067691 * A067693 A067694 A067695

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 04, 2002

STATUS

approved

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Last modified December 7 22:57 EST 2016. Contains 278899 sequences.