A051351 -id:A051351 - cp's OEIS frontend

A095406 Numbers n such that Sum-of-digits-of-n < Sum-of-digits-of-all-distinct-prime-factors-of-n.

10, 12, 14, 15, 20, 21, 30, 34, 35, 38, 40, 42, 50, 51, 57, 60, 63, 70, 74, 90, 91, 95, 100, 102, 104, 105, 106, 110, 111, 112, 114, 115, 116, 118, 119, 120, 122, 123, 126, 130, 132, 133, 134, 140, 141, 142, 145, 146, 150, 152, 153, 154, 158, 161, 170, 171, 174

Offset: 1

Labos Elemer, Jun 21 2004

			n=38: digit sum=11, prime factor-digit sum=2+1+9=12>11, so 38 is here;
n=10^j:digit sum=1, prime factor-digit sum=2+5=7?1. so 10^j is here for all j [this implies that the sequence is infinite].

Cf. A007953, A051351, A095402, A095403, A095404, A095405.

ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] a=Table[sd[w], {w, 1, 256}];b=Table[sdp[w], {w, 1, 150}];b-a; Flatten[Position[Sign[b-a], -1]]
Select[Range[200],Total[IntegerDigits[#]]Harvey P. Dale, May 06 2012 *)

Solutions to A007953[x] < A095402[x].

A071421 a(n) = a(n-1) + sum of decimal digits of n^n.

Original entry on oeis.org

1, 5, 14, 27, 38, 65, 90, 127, 172, 173, 214, 268, 326, 378, 477, 565, 663, 771, 898, 929, 1046, 1194, 1340, 1493, 1644, 1798, 1987, 2150, 2317, 2380, 2564, 2769, 2976, 3190, 3450, 3720, 3991, 4256, 4562, 4674, 4982, 5297, 5610, 5935, 6241, 6593, 6967

Offset: 1

Labos Elemer, May 27 2002

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A037123, A000788, A051351.

s=0; Do[s=s+Apply[Plus, IntegerDigits[n^n]]; Print[s], {n, 1, 128}]
nxt[{n_,a_}]:={n+1,a+Total[IntegerDigits[(n+1)^(n+1)]]}; NestList[nxt,{1,1},50][[All,2]] (* Harvey P. Dale, Dec 11 2016 *)

A071422 a(n) = a(n-1) + sum of decimal digits of sigma(n), the sum of divisors of n.

Original entry on oeis.org

1, 4, 8, 15, 21, 24, 32, 38, 42, 51, 54, 64, 69, 75, 81, 85, 94, 106, 108, 114, 119, 128, 134, 140, 144, 150, 154, 165, 168, 177, 182, 191, 203, 212, 224, 234, 245, 251, 262, 271, 277, 292, 300, 312, 327, 336, 348, 355, 367, 379, 388, 405, 414, 417, 426, 429

Offset: 1

Labos Elemer, May 27 2002

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A037123, A000788, A051351.

Partial sums of A067342.

s=0; Do[s=s+Apply[Plus, IntegerDigits[DivisorSigma[1, n]]]; Print[s], {n, 1, 128}]
nxt[{n_,a_}]:={n+1,a+Total[IntegerDigits[DivisorSigma[1,n+1]]]}; Transpose[ NestList[nxt,{1,1},60]][[2]] (* Harvey P. Dale, Jan 25 2013 *)

A283556 Digital root of the sum of the first n primes.

Original entry on oeis.org

0, 2, 5, 1, 8, 1, 5, 4, 5, 1, 3, 7, 8, 4, 2, 4, 3, 8, 6, 1, 9, 1, 8, 1, 9, 7, 9, 4, 3, 4, 9, 1, 6, 8, 3, 8, 6, 1, 2, 7, 9, 8, 9, 2, 6, 5, 6, 1, 8, 1, 5, 4, 9, 7, 6, 2, 4, 3, 4, 2, 4, 8, 4, 5, 1, 8, 1, 8, 3, 8, 6, 8, 7, 5, 9, 1, 6, 8, 9, 5, 9, 5, 3, 2, 3, 1, 3, 2, 9, 2, 6, 5, 7, 8, 4, 8, 7, 3, 2, 3

Offset: 0

Dimitris Valianatos, Mar 10 2017

			For n=3, a(3)=1 because the sum of the first 3 primes is 10 and the sum of digits of 10 is 1.

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A007504, A010888, A051351.

0, op(subs(0=9, ListTools:-PartialSums(select(isprime, [2,seq(i,i=3..1000,2)])) mod 9)); # Robert Israel, Mar 30 2017

With[{nn = 78}, {0}~Join~Table[NestWhile[Total@ IntegerDigits@ # &, #, # >= 10 &] &@ Total@ Take[#, n], {n, nn}] &@ Array[Prime, nn]] (* Michael De Vlieger, Mar 15 2017 *)

{
p=0;print1(p", ");
forprime(n=2,1000,
         p+=n;
         while(p>9,p=sumdigits(p))
         ;print1(p", ")
        )
}

from sympy import primerange
from itertools import accumulate
prime_sum = [0] + list(accumulate(primerange(2, 1000)))
def dig_root(n): return 1+(n-1)%9
def a(n):
    return 0 if n<1 else dig_root(prime_sum[n])
print([a(n) for n in range(101)]) # Indranil Ghosh, Mar 30 2017

a(n) = ((A007504(n) - 1) mod 9) + 1.
a(n) = ((A051351(n) - 1) mod 9) + 1.
a(n) = A010888(A007504(n)). - Michel Marcus, Mar 26 2017

Corrected by Robert Israel, Mar 30 2017

A058196 Sum of digits of first 10^n primes.

Original entry on oeis.org

2, 57, 1111, 17024, 224155, 2674957, 31352962, 363506969, 4127383480, 45630284509, 502160313778

Offset: 0

Robert G. Wilson v, Nov 27 2000

Cf. A051351, A057573.

NextPrime[ n_Integer ] := Module[ {k}, k = n + 1; While[ ! PrimeQ[ k ], k++ ]; k ]; c = d = p = q = 0; Do[ While[ d++; d <= 10^n, q = NextPrime[ q ]; p = p + Apply[ Plus, RealDigits[ q ][ [ 1 ] ] ]; If[ PrimeQ[ p ], c++ ] ]; d--; Print[ p ], {n, 0, 10}]

a(n) = {my(k = 0, s = 0, pow = 10^n); forprime(p = 2, , k++; s += sumdigits(p); if(k == pow, break)); s;} \\ Amiram Eldar, Jun 03 2024

a(9)-a(10) from Amiram Eldar, Jun 03 2024

A071122 a(n) = a(n-1) + sum of decimal digits of 2^n.

Original entry on oeis.org

2, 6, 14, 21, 26, 36, 47, 60, 68, 75, 89, 108, 128, 150, 176, 201, 215, 234, 263, 294, 320, 345, 386, 423, 452, 492, 527, 570, 611, 648, 695, 753, 815, 876, 935, 999, 1055, 1122, 1193, 1254, 1304, 1350, 1406, 1464, 1526, 1596, 1664, 1737, 1802, 1878, 1958

Offset: 1

Labos Elemer, May 27 2002

Cf. A037123, A000788, A051351, A071317, A071121.

s=0; Do[s=s+Apply[Plus, IntegerDigits[2^n]]; Print[s], {n, 1, 128}]

A071123 a(n) = a(n-1) + sum of decimal digits of n!.

Original entry on oeis.org

1, 3, 9, 15, 18, 27, 36, 45, 72, 99, 135, 162, 189, 234, 279, 342, 405, 459, 504, 558, 621, 693, 792, 873, 945, 1026, 1134, 1224, 1350, 1467, 1602, 1710, 1854, 1998, 2142, 2313, 2466, 2574, 2763, 2952, 3096, 3285, 3465, 3681, 3888, 4104, 4329, 4563, 4788

Offset: 1

Labos Elemer, May 27 2002

Cf. A037123, A000788, A051351.

s=0; Do[s=s+Apply[Plus, IntegerDigits[n! ]]; Print[s], {n, 1, 128}]

cp's OEIS Frontend

A095406 Numbers n such that Sum-of-digits-of-n < Sum-of-digits-of-all-distinct-prime-factors-of-n.

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A071421 a(n) = a(n-1) + sum of decimal digits of n^n.

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A071422 a(n) = a(n-1) + sum of decimal digits of sigma(n), the sum of divisors of n.

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A283556 Digital root of the sum of the first n primes.

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A058196 Sum of digits of first 10^n primes.

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A071122 a(n) = a(n-1) + sum of decimal digits of 2^n.

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A071123 a(n) = a(n-1) + sum of decimal digits of n!.

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