A073262 -id:A073262 - cp's OEIS frontend

A053781 Numbers k that divide the sum of the first k composite numbers.

1, 2, 3, 7, 11, 71, 107, 115, 139, 155, 681, 1671, 4876, 21464, 30046, 311271, 788749, 10893662, 20743270, 134568163, 163879554, 920161004, 6364787032, 21400458779, 47934932406, 56133884369, 288050185452, 536023681676, 1484061538595

Offset: 1

G. L. Honaker, Jr., Mar 29 2000

nonn

E. Friedman, What is special about this number?, see 681.

Cf. A002808, A073262, A073263.

c = s = 0; Do[ If[ !PrimeQ[n], c++; s = s + n; If[ Mod[s, c] == 0, Print[c]]], {n, 2, 10^9}] (* Robert G. Wilson v, Nov 23 2004 *)

lista(nn) = {s = 0; n = 0; forcomposite(c=0, nn, s += c; n++; if (! (s % n), print1(n, ", ")););} \\ Michel Marcus, Mar 15 2015

Numbers k such that k divides A053767(k). - Robert G. Wilson v, Nov 24 2004

a(19)-a(22) from Robert G. Wilson v, Nov 24 2004
a(23)-a(26) from Sean A. Irvine, Oct 01 2009
a(27)-a(29) from Donovan Johnson, Jul 06 2010

A073263 Integer quotients of partial sum of first n composite and n (see A053781).

Original entry on oeis.org

4, 5, 6, 9, 12, 52, 75, 80, 95, 105, 422, 1002, 2841, 12165, 16944, 170997, 430041, 5844984, 11095683, 71438394, 86938085, 485470043, 3341061731, 11203279551, 25053055391, 29329179630, 150058180590, 278953774325, 771115150044

Offset: 1

Labos Elemer, Jul 22 2002

nonn

Cf. A002808, A053781, A073255-A073262.

s=0; Do[s=s+FixedPoint[n+PrimePi[ # ]+1&, n]; If[IntegerQ[s/n], k=k+1; t[[k]]=s/n; Print[s/n]], {n, 1, 12000000}]

a(n)=A073262(n)/A053781(n)

a(17) - a(19) from Klaus Brockhaus, Aug 12 2009
a(20)-a(26) from Ray Chandler, Jul 19 2010
a(27)-a(29) from Donovan Johnson, May 23 2011

A179861 a(n) is the sum of the first A179859(n) noncomposites.

Original entry on oeis.org

1, 6, 42, 143100, 775304, 1891890, 14646554832, 130985694070, 188757015148, 419047914740, 1055777525624570390, 1492138298614167680, 70288308055831268412, 91779857115464381780, 571686203669195590338, 56978071532766214007450, 83023388015844408083484

Offset: 1

Ray Chandler, Jul 29 2010

nonn

A variant of A050247 (primes), A073262 (composites) and A164280 (nonprimes).

			A179859(3) = 7; sum of first 7 noncomposites is 42, so a(3) = 42.

Cf. A008578 (noncomposites), A014284 (sum of first n noncomposites).

Cf. A050247, A073262, A164280, A179859, A179860.

a(n) = A014284(A179859(n)) = A179859(n) * A179860(n).

a(16)-a(17) from Amiram Eldar, May 24 2024

cp's OEIS Frontend

A053781 Numbers k that divide the sum of the first k composite numbers.

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A073263 Integer quotients of partial sum of first n composite and n (see A053781).

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Extensions

A179861 a(n) is the sum of the first A179859(n) noncomposites.

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