

A067692


a(n) = sum{d*t : 0<d<=t<=n and dn and tn}.


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
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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.


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 A173230
Adjacent sequences: A067689 A067690 A067691 * A067693 A067694 A067695


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Feb 04, 2002


STATUS

approved



