editing

approved

a = {}; c = 0; For[n = 4, n < 10000, n++, If[Sum[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}] == 2, c++; If[Plus @@ IntegerDigits[c] == Plus @@ IntegerDigits[n], AppendTo[a, c]]]]; a - _(* _Stefan Steinerberger_, Dec 29 2007 *)

approved

editing

SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Select[Range@ 1000, fQ@# &] (* _Robert G. Wilson v _ *)

editing

approved

nn=5000; With[{sp=Select[Range[nn], PrimeOmega[#]==2&]}, Select[Range[ Length[sp]], Total[ IntegerDigits[sp[[#]]]] ==Total[ IntegerDigits[#]]&]] (* Harvey P. Dale, Oct 15 2012 *)

approved

editing

a = {}; c = 0; For[n = 4, n < 10000, n++, If[Sum[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}] == 2, c++; If[Plus @@ IntegerDigits[c] == Plus @@ IntegerDigits[n], AppendTo[a, c]]]]; a - _Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), _, Dec 29 2007

Corrected and extended by _Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) _ and Robert G. Wilson v, Dec 29 2007

_Jonathan Vos Post (jvospost3(AT)gmail.com), _, Dec 27 2007

Corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and _Robert G. Wilson v (rgwv(AT)rgwv.com), _, Dec 29 2007

base,easy,nonn,less,new

Jonathan Vos Post (jvospost2jvospost3(AT)yahoogmail.com), Dec 27 2007

Numbers n such that the sum of digits of n-th semiprime equals sum of digits of n.

5, 6, 19, 40, 41, 42, 70, 71, 85, 89, 128, 148, 149, 166, 199, 246, 257, 271, 285, 327, 339, 346, 448, 449, 469, 484, 566, 592, 605, 617, 634, 643, 644, 676, 682, 694, 710, 713, 719, 740, 748, 751, 752, 753, 782, 793, 794, 797, 798, 815, 890, 901, 905, 961

1,1

This is to A033549 as semiprimes A001358 are to primes A000040.

A007953(A001358(a(n))) = A007953(a(n)).

a(1) = 5 because semiprime(5) = 14, whose sum of digits is 5, the same as its index as a semiprime.

a = {}; c = 0; For[n = 4, n < 10000, n++, If[Sum[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}] == 2, c++; If[Plus @@ IntegerDigits[c] == Plus @@ IntegerDigits[n], AppendTo[a, c]]]]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Dec 29 2007

SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Select[Range@ 1000, fQ@# &] (* Robert G. Wilson v *)

Cf. A001358, A007953, A033549.

base,easy,nonn,less

Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 27 2007

Corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 29 2007

approved