A366507
Numbers k such that the sum of the digits of k times the square of the sum of the digits cubed of k equals k.
Original entry on oeis.org
1, 4147200, 12743163, 21147075, 39143552, 52921472, 156754936, 205889445, 233935967
Offset: 1
4147200 = (4+1+4+7+2)*(4^3+1+4^3+7^3+2^3)^2 = 18*230400.
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niven12()={for(a=0,9,for(b=0,9,for(c=0,9,for(d=0,9,for(e=0,9,for(f=0,9,for(g=0,9,for(h=0,9,for(i=0,9,for(j=0,9,if((a+b+c+d+e+f+g+h+i+j)*(a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3+i^3+j^3)^2==1000000000*a+100000000*b+10000000*c+1000000*d+100000*e+10000*f+1000*g+100*h+10*i+j,print1(1000000000*a+100000000*b+10000000*c+1000000*d+100000*e+10000*f+1000*g+100*h+10*i+j,";"))))))))))))}
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isok(k) = my(d=digits(k)); vecsum(d)*sum(i=1, #d, d[i]^3)^2 == k; \\ Michel Marcus, Oct 12 2023
A366512
Numbers k such that the square of the sum of the digits times the sum of the cubes of the digits equals k.
Original entry on oeis.org
1, 32144, 37000, 111616, 382360
Offset: 1
32144 = ((3+2+1+4+4)^2)*(3^3 + 2^3 + 1^3 + 4^3 + 4^3) = 196*164.
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Select[Range[10^6], #1 == Total[#2]^2*Total[#2^3] & @@ {#, IntegerDigits[#]} &] (* Michael De Vlieger, Mar 25 2024 *)
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niven23()={for(a=0,9,for(b=0,9,for(c=0,9,for(d=0,9,for(e=0,9,for(f=0,9,for(g=0,9,for(h=0,9,if((a+b+c+d+e+f+g+h)^2*(a^3+b^3+c^3+d^3+e^3+f^3+g^3+h^3)==10000000*a+1000000*b+100000*c+10000*d+1000*e+100*f+10*g+h,print1(10000000*a+1000000*b+100000*c+10000*d+1000*e+100*f+10*g+h,", "))))))))))}
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isok(k) = my(d=digits(k)); vecsum(d)^2*sum(i=1, #d, d[i]^3) == k; \\ Michel Marcus, Oct 12 2023
A368939
Numbers k such that the sum of the digits times the sum of the fourth powers of the digits equals k.
Original entry on oeis.org
0, 1, 182380, 444992
Offset: 1
182380 = (1+8+2+3+8)*(1^4 + 8^4 + 2^4 + 3^4 + 8^4) = 22*8290.
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Select[Range[0,10^7],#==Total[IntegerDigits[#]]*Total[IntegerDigits[#]^4]&] (* James C. McMahon, Jan 11 2024 *)
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niven14(k) = my(d=digits(k)); vecsum(d)*sum(i=1, #d, d[i]^4) == k;
for(k=1,10^7,if(niven14(k)==1,print1(k,", ")))
A375343
Numbers which are the sixth powers of their digit sum.
Original entry on oeis.org
0, 1, 34012224, 8303765625, 24794911296, 68719476736
Offset: 1
68719476736 = (6+8+7+1+9+4+7+6+7+3+6)^6 = 64^6.
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for (k=0, sqrtnint(10^13,6), if (k^6 == sumdigits(k^6)^6, print1(k^6, ", ")); )
A379767
Triangle read by rows: row n lists numbers which are the n-th powers of their digit sum.
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 81, 0, 1, 512, 4913, 5832, 17576, 19683, 0, 1, 2401, 234256, 390625, 614656, 1679616, 0, 1, 17210368, 52521875, 60466176, 205962976, 0, 1, 34012224, 8303765625, 24794911296, 68719476736, 0, 1, 612220032, 10460353203, 27512614111, 52523350144, 271818611107, 1174711139837, 2207984167552, 6722988818432
Offset: 1
Triangle begins:
1 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;
2 | 0, 1, 81;
3 | 0, 1, 512, 4913, 5832, 17576, 19683;
4 | 0, 1, 2401, 234256, 390625, 614656, 1679616;
5 | 0, 1, 17210368, 52521875, 60466176, 205962976;
6 | 0, 1, 34012224, 8303765625, 24794911296, 68719476736;
7 | 0, 1, 612220032, 10460353203, 27512614111, 52523350144, 271818611107, 1174711139837, 2207984167552, 6722988818432;
8 | 0, 1, 20047612231936, 72301961339136, 248155780267521;
9 | 0, 1, 3904305912313344, 45848500718449031, 150094635296999121;
...
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R(n) = for(j=2,oo, if((j*9)^n <10^j, return(j)));
row(n) = my(L=List()); for (k=0, sqrtnint(10^R(n),n), if (k^n == sumdigits(k^n)^n, listput(L, k^n))); Vec(L)
A370250
Numbers k such that the sum of the digits times the square of the sum of the fourth powers of the digits equals k.
Original entry on oeis.org
0, 1, 5873656512, 7253758561, 29961747275
Offset: 1
7253758561 = (7+2+5+3+7+5+8+5+6+1)*(7^4 + 2^4 + 5^4 + 3^4 + 7^4 + 5^4 + 8^4 + 5^4 + 6^4 + 1^4)^2 = 49*148035889 = 7253758561.
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niven142(k) = my(d=digits(k)); vecsum(d)*sum(i=1, #d, d[i]^4)^2 == k;
for(k=0,10^12,if(niven142(k)==1,print1(k, ", ")))
Showing 1-6 of 6 results.
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