A065132
Arithmetic mean of first n terms of A008472 is an integer.
Original entry on oeis.org
2, 13, 134, 167, 2239, 62268, 75255, 135681, 439867, 18139940, 23671044, 40892256, 312083956, 724031017, 1990127567, 2144843867, 2588619526, 7439533243, 15054156002, 54892225873, 69959798320, 79760490898, 282311798922
Offset: 1
Sum of first 13 terms of A008472 gives A024924(13) = 65 which is divisible by n = 13, so 13 is here: 0+2+3+2+5+5+7+2+3+7+11+5+13 = 65 = 13*5 = A024924(13).
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s=0; Do[s=s+sp[n]; If[IntegerQ[n/25000], Print[n]]; If[IntegerQ[s/n], Print[{n, s, s/n}]], {n, 2, 4000000}] where sp[n]=A008472(n).
A136025
Sum of distinct proper prime divisors of odd integers below 10^n.
Original entry on oeis.org
3, 373, 24307, 1691682, 127867801, 10233538789, 850896280551, 72812857079241, 6363727756215813, 565232434009370012, 50843507342073211151, 4620323131256374760046, 423405369424475640435621, 39074878176445767411791424
Offset: 1
a(0)=3 because the only odd N <=10^1-1 having a prime factor is 9 and its factor is 3 and sum is 3.
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A105221 := proc(n) local a,ifs,p; ifs := ifactors(n)[2] ; a := 0 ; for p in ifs do if op(1,p) <> 1 and op(1,p) <> n then a := a+op(1,p) ; fi ; od: RETURN(a) ; end: A136025 := proc(n) local a,k ; a := 0 ; for k from 5 to 10^n-1 by 2 do a := a+A105221(k) ; od: RETURN(a) ; end: for n from 1 do print(A136025(n)); od: # R. J. Mathar, Jan 29 2008
A143853
Primes p that divide the sum of their remainders modulo all smaller composites (=A233131(p)).
Original entry on oeis.org
2, 3, 23, 53, 613, 490537
Offset: 1
Composites smaller than 23 are 4,6,8,9,10,12,14,15,16,18,20,21 and 22. 23 is congruent to 3,5,7,5,3,11,9,8,7,5,3 and 2 modulo these numbers respectively. The sum of these residues is 69. This is a multiple of 23, so 23 is in the sequence.
Showing 1-3 of 3 results.
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