A125826
Numbers m that divide 2^7 + 3^7 + 5^7 + ... + prime(m)^7.
Original entry on oeis.org
1, 25, 1677, 21875, 538513, 1015989, 18522325, 1130976595, 1721158369, 561122374231, 1763726985077, 2735295422833, 7631117283951, 22809199833151, 46929434362563, 49217568518075, 151990420653423, 174172511353413, 1258223430425543
Offset: 1
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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s = 0; Do[s = s + Prime[n]^7; If[ Mod[s, n] == 0, Print[n]], {n, 25000}]
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s=0; n=0; forprime(p=2, 4e9, s+=p^7; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Mar 16 2011
A125827
Numbers m that divide 2^11 + 3^11 + 5^11 + ... + prime(m)^11.
Original entry on oeis.org
1, 25, 59, 2599, 6195, 421407, 11651191, 19293221, 255136097, 1820015683, 2183556659, 7993872143, 9850779563, 2006892138335, 2649677145789, 6645858099781, 318039538085101, 414996765110825
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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s = 0; Do[s = s + Prime[n]^11; If[ Mod[s, n] == 0, Print[n]], {n, 7000}]
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s=0; n=0; forprime(p=2, 4e9, s+=p^11; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Mar 20 2011
A131263
Numbers k such that k divides 2^9 + 3^9 + 5^9 + ... + prime(k)^9.
Original entry on oeis.org
1, 281525, 1011881, 13721649, 309777093, 417800903, 12252701193, 27377813605, 37762351523, 245773819141, 51230573255953, 82578361848569, 277900491430385
Offset: 1
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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s = 0; Do[s = s + Prime[n]^9; If[ Mod[s, n] == 0, Print[n]], {n, 1100000}]
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s=0; n=0; forprime(p=2, 1e9, s+=p^9; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Apr 14 2011
A131264
Numbers k such that k divides 2^10 + 3^10 + 5^10 + ... + prime(k)^10.
Original entry on oeis.org
1, 269, 41837, 36626159, 154578947, 2155054465, 19410890423, 30691222355, 247555091527, 2201220228533, 227735225320519, 478444326378215
Offset: 1
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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s = 0; Do[s = s + Prime[n]^10; If[ Mod[s, n] == 0, Print[n]], {n, 1000000}]
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s=0;n=0;forprime(p=2, 1e9, s+=p^10; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Apr 14 2011
A131272
Numbers k such that k divides Sum_{j=1..k} prime(j)^12.
Original entry on oeis.org
1, 37, 7187, 3140407, 4986959, 5139161, 751213639, 163007938237, 5134788477263, 36197588005399, 940901369608517
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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s = 0; Do[s = s + Prime[n]^12; If[ Mod[s, n] == 0, Print[n]], {n, 1000000}]
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s=0; n=0; forprime(p=2,1e9,s+=p^12; if(s%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Apr 14 2011
A131274
Numbers m such that m divides Sum_{k=1..m} prime(k)^14.
Original entry on oeis.org
1, 295, 455, 4361, 10817, 132680789, 334931875, 957643538339, 82185210732157
Offset: 1
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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s = 0; Do[s = s + Prime[n]^14; If[ Mod[s, n] == 0, Print[n]], {n, 660000000}] (* Robert G. Wilson v, Jul 01 2007 *)
With[{nn=11000},Select[Thread[{Accumulate[Prime[Range[nn]]^14],Range[ nn]}],Divisible[ #[[1]],#[[2]]]&]][[All,2]] (* The program generates the first 5 terms of the sequence. To generate more, increase the value of nn. *) (* Harvey P. Dale, Jun 25 2021 *)
A131275
Numbers k such that k divides Sum_{j=1..k} prime(j)^15.
Original entry on oeis.org
1, 17, 25, 31, 1495, 5555, 8185, 8647, 106841, 187329, 345377, 1811351, 2179119, 2863775, 6368703, 10250821, 59137893, 337430815, 11349203711, 183233304195, 12538656829431, 40154010310477, 1761333303516473
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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s = 0; Do[s = s + Prime[n]^15; If[ Mod[s, n] == 0, Print[n]], {n, 400000}]
With[{nn = 3*10^6},Select[Thread[{Accumulate[Prime[ Range[nn]]^15],Range[ nn]}],Divisible[#[[1]], #[[2]]] &]][[All, 2]] (* This will generate the first 14 terms of the sequence; to generate more, increase the value of nn, but it may take a long time to run. *) (* Harvey P. Dale, Oct 03 2016 *)
A131276
Numbers m such that m divides Sum_{k=1..m} prime(k)^16.
Original entry on oeis.org
1, 3131, 6289, 323807, 443371, 83802527023, 4076111200313
Offset: 1
Cf.
A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
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s = 0; Do[s = s + Prime[n]^16; If[ Mod[s, n] == 0, Print[n]], {n, 500000}]
Transpose[Select[With[{nn=500000},Thread[{Range[nn],Accumulate[ Prime[ Range[nn]]^16]}]], Divisible[ #[[2]],#[[1]]]&]][[1]]
A131277
Numbers m that divide Sum_{k=1..m} prime(k)^17.
Original entry on oeis.org
1, 395191, 697717, 1078323, 2050797, 10543929, 386099691, 2467825171, 4488040933, 17387575533, 39641205433, 825688143387, 2800262033655, 3214748608393, 5174884331693, 16485974355373, 20683624349423, 34390023299149, 629341300687639
Offset: 1
Cf.
A085450 (smallest m > 1 that divide Sum_{k=1..m} prime(k)^n).
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s = 0; Do[s = s + Prime[n]^17; If[ Mod[s, n] == 0, Print[n]], {n, 1100000}]
A131278
Numbers m such that m divides the sum of the 18th powers of the first m primes.
Original entry on oeis.org
1, 37, 265, 17207, 9382589, 970248431, 2427811793, 156281194823, 2955922292131, 372012276565795
Offset: 1
Cf.
A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
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s = 0; Do[s = s + Prime[n]^18; If[ Mod[s, n] == 0, Print[n]], {n, 10^6}]
With[{nn = 18000}, Transpose[With[{c = Thread[{Range[nn], Accumulate[Prime[ Range[nn]]^18]}]}, Select[c, Divisible[Last[#], First[#]] &]]][[1]]] (* Harvey P. Dale, Dec 19 2011 *)
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